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<$> * o ft o 







An Introduction 
to 

Modern Logic 



BY 



RUPERT CLENDON LODGE, M. A. 

n 

ASSISTANT PROFESSOR OF PHILOSOPHY 
IN THE UNIVERSITY OF MINNESOTA. 

SOMETIME JOHN LOCKE SCHOLAR IN MENTAL PHILOSOPHY 
IN THE UNIVERSITY OF OXFORD. 



THE PERINE BOOK COMPANY 
Minneapolis. 



\9* 



# 



Copyright 

The Perine Book Company, 

Minneapolis, 

1920. 



MAk 29 1920 



©CLA566228 



PREFACE 

This book is intended to be precisely what the title implies 
— an introduction to modern logic. By ''modern" logic is 
understood that body of logical theories and methods which is 
usually associated with the names of Lotze, Sigwart, Bradley, 
Bosanquet, Wundt, Erdmann, and Dewey. The writer has 
endeavored to place himself in the center of this movement 
taken as a whole, and to set forth the characteristic doctrines 
of the modern school, so far as this has seemed possible in a 
book which is professedly introductory. The traditional or 
Aristotelian logic, which has played so great a part in the 
past history of thought, is entirely omitted from consideration, 
as are also symbolic logic and the various attempts at invent- 
ing a logical calculus. For all such omissions, as well as for 
what is included, the sole justification is the nature of an 
introductory treatise. It has seemed best to avoid polemics 
on the one hand, and an unmanageable multiplicity of hypoth- 
eses on the other, in favor of a certain singleness of purposi 
and organic unity of thought. 

The exercises and suggestions for further reading at the 
end of the different chapters should be regarded as an integral 
portion of the book. To attempt to study logic without work- 
ing one's way through appropriate exercises is like trying to 
study mathematics without solving problems, and leads inevit- 
ably to a certain superficiality of mental grasp which it is 
the avowed aim of logical treatises to fight and destroy. So 
also to confine one's reading to a single text-book is to shut 
one's mind to the interest and infinite variety, as well as to 
the concreteness and usefulness, of an important branch of 
modern science. 

The writer's obligations are too numerous to mention. The 
influence of Plato and Kant, on the one hand, and of Locke, 
Hume, and Mill, on the other, is sufficiently obvious. But in 
the case of more recent writers and teachers it would be 
invidious to single out any one group. The chapter headings 
of Part III are in large part taken from Wundt's AUgemeine 
Methodenlehre, but for the contents of the chapters in question 
Wundt is in no special sense responsible. 
University of Minnesota. 
September, 1918. 



SYNOPSIS 

Chapter 
Part I 

JUDGMENT 

The elements and chief stages of judgment I 

The sensory element in judgment II 

Sensory validity in judgment Ill 

The intellectual element — identity, difference, 

and organisation IV-VIII 

Intellectual validity in judgment IX 

General validity — theory of judgment X 

Part II 
INFERENCE 

General characteristics of inference XI 

(a) dependent or hypothetical XII 

(b) analytical and expansive XIII 

(c) novelty-seeking XIV 

(d) constructive and systematic XV 

Sensory and intellectual elements in inference. . XVI 

Validity — theory of inference XVII 

Part III 

SCIENTIFIC METHOD 

Methods of investigation, and forms of exposi- 
tion 

(a) Analysis and synthesis XIX-XXI 

(b) Abstraction and determination XXII-XXIII 

(c) Induction and deduction XXIV-XXVI 

(d) Definition XXVII 

(e) Classification XXVIII 

(f) Proof XXIX 

(g) Fallacy XXX 

(h) System of the sciences XXXI 

Theory of scientific method XXXII 

vii 



CONTENTS 

INTRODUCTION Page 

The logical attitude of mind — The study of logic — Pre- 
liminary definition of logic 1 

PART I 

Chapter I 

JUDGMENT 

The simplest judgments — The elements of judgment — 

The chief stages of judgment 9 

Chapter II 

The sensory element — In judgments of perception — In 
judgments of experience — In symbolic judgments — In 
transcendent judgments — Summary 17 

Chapter III 

The question concerning sensory validity — In judgments 
of perception — In judgments of experience — In sym- 
bolic judgments — In transcendent judgments — Con- 
clusion 23 

Chapter IV 

The intellectual element — In judgments of perception — 
In judgments of experience — In symbolic judgments 
— In transcendent judgments — Conclusion ... 37 

Chapter V 

Identity or sameness — In judgments of perception — In 
judgments of experience — In symbolic judgments — 
In transcendent judgments — Conclusion .... 46 

Chapter VI 

Difference — In judgments of perception — In judgments of 
experience — In symbolic judgments — In transcendent 
judgments — Conclusion 54 

ix 



x CONTENTS 

Chapter VII Page 

Internal organisation — In judgments of perception — In 
judgments of experience — In symbolic judgments — In 
transcendent judgments — Conclusion 65 

Chapter VIII 

External organisation — In judgments of perception — In 
judgments of experience — In symbolic judgments — In 
transcendent judgments — Conclusion 79 

Chapter IX 

The question of intellectual validity— In judgments of per- 
ception — In judgments of experience — In symbolic 
judgments — In transcendent judgments — Conclusion 92 

Chapter X 

The problem of general validity — Idealism — Sensualism 

— The solution — Application — Theory of judgment 101 

Appendix 
Is negation subjective? — Is negation indefinite? . . . 108 

PART II 

Chapter XI 

INFERENCE 

The general characteristics of inference — Dependence — 
Analytic expansion — Novelty — Systematic construc- 
tiveness — Conclusion 119 

Chapter XII 

Dependent or hypothetical nature of inference — Kinds of 
dependence — From cause — From absence of cause — 
From effect — From absence of effect — Conclusion — 
Further consideration — Conclusion concerning em- 
pirical cases — Hypothetical versus categorical — Con- 
cluding summary 127 



CONTENTS xi 

Chapter XIII Page 

General nature of analysis in inference — Specific features 

of analysis — Analysis and intuition — Conclusion . 138 

Chapter XIV 

The problem of novelty in inference — Sensory novelty — 
Intellectual novelty — The field of relations — Latent 
knowledge — Arguing to the unknown? — Conclusion 148 

Chapter XV 

Examples of systematic constructiveness in inference — 
How does inference construct? — Validity of infer- 
ential constructions — Conclusion 160 

Chapter XVI 

The problem of describing inference — The sensory ele- 
ments — In dependence, analytic expansion, novelty, 
and systematic constructiveness — The intellectual ele- 
ments — In dependence, analytic expansion, novelty, 
and systematic constructiveness — Summary . . . 169 

Chapter XVII 

The problem of the validity of inference — Dependence — 
Analytic expansion — Novelty — Constructiveness — 
Theory of inference 184 



PART III 

Chapter XVIII 
SCIENTIFIC METHOD 

Scientific and unscientific method — Methods of investiga- 
tion — Analysis, abstraction, determination, synthesis, 
induction, deduction — Summary — Forms of exposi- 
tion — Definition, classification, proof, system of the 
sciences — Summary 197 



xii CONTENTS 

Chapter XIX Page 

Nature of analysis — Aim of analysis — How far realisable? 
— With man-made structures and mental models, and 
with natural phenomena — Methods of scientific analy- 
sis — Mathematical and causal — Validity of such 
methods — Summary 208 

Chapter XX 

Nature of synthesis — Aim of synthesis — How far realis- 
able? — With mind-made entities, and with natural 
phenomena — Methods of scientific synthesis — Mathe- 
matical and causal — Validity of these methods — 
Summary 218 

Chapter XXI 

Analysis and synthesis — Is analysis synthetical? — Mind- 
made entities, and natural phenomena — Is synthesis 
analytical? — Mind-made entities, and natural 
phenomena — Summary — Differences between analysis 
and synthesis — Apparent starting-point, conclusion, 
and method — Is synthesis a more advanced method? 
— Summary 230 

Chapter XXII 

Nature of abstraction — Aim of abstration — How far real- 
isable? — With mind-made entities, and with natural 
phenomena — Types of abstraction — Validity of these 
methods — Summary 243 



Chapter XXIII 

Nature of determination — Aim of determination — How far 
realisable? — With mind-made entities, and with na- 
tural phenomena — Validity of determination — Sum- 
mary — Abstraction and determination — Does abstrac- 
tion involve determination? — Does determination in- 
volve abstraction? — Comparison with analysis and 
synthesis 252 



CONTENTS xiii 

Chapteb XXIV Page 

Nature of induction — Aim of induction — How far real- 
isable? — With mind-made entities, and with natural 
phenomena — Types of inductive method — Validity of 
induction — Summary 263 

Chapter XXV 

Nature of deduction — Aim of deduction — How far realis- 
able? — With mind-made entities, and with natural 
phenomena — Types of deduction — Validity of deduc- 
tion — Summary 273 

Chapter XXVI 

Induction and deduction — Does induction involve deduc- 
tion? — Docs deduction involve induction? — The induc- 
tive-deductive method — The nature of scientific 
investigation 283 

Chapter XXVII 

Nature of definition — Aim of definition — How far realis- 
able? — With mind-made objects, and with natural 
phenomena — Types of definition — Validity of defini- 
tion — Summary and conclusion 292 

Chapter XXVIII 

Nature of classification — Aim of classification — How far 
realisable? — With mind-made entities, and with 
natural phenomena — Types of classification — Validity 
of classification — Function of classification in exposi- 
tion — Summary 305 

Chapter XXIX 

Nature of proof — Aim of proof — How far realisable? 
— With mind-made entities, and with natural phe- 
nomena — Validity of proof — Types of proof — Sum- 
mary 316 



xiv CONTENTS 

Chapter XXX Page 

Definition of fallacy — Occasions of fallacy — Scope of fal- 
lacy — Source of fallacy — Types of fallacy .... 326 

Chapter XXXI 

Nature of a system of the sciences — Aim of such system- 
atisation — How far realisable? — Types of such sys- 
tematisation — Validity of such systematisation — 
Summary 336 

Chapter XXXII 

Description of scientific method — Sensory elements in 
scientific method — Intellectual elements in scientific 
method — Summary — Validity of scientific method — 
In dealing with mind-made entities, and with 
natural phenomena — Conclusion 346 

Index I 355 

Index II . - .357 



INTRODUCTION 

The Logical Attitude of Mind. — The natural behavior of 
men, as of other animals, is not logical, but instinctive, We 
tend to react to most of the concrete situations of life in a 
way determined by inherited neural dispositions rather than 
by "reasoning things out." The life of most men appears to 
be spent in acquiring food and shelter, a family, and money 
to expend in purchasing houses, automobiles, education and 
luxuries for the rising generation, and insurance against dis- 
aster. That is to say, the main outlines of life — power, love, 
and protection of the family — are fixed in the main by inher- 
ited racial tendencies, and it is around these that almost all 
our activities are grouped. And it is not only the outlines 
which are instinctive. Nearly all our more detailed everyday 
experiences are of the same kind. Taking meals, sleeping, 
feeling aggressive or timid in our work and play, day-dream- 
ing as we plan for the morrow, feeling elated or depressed at 
the progress we are making — all these experiences are funda- 
mentally instinctive, and we should be seriously puzzled, if 
we were called upon to account for them in purely rational 
terms. To the average man, indeed, it never even occurs to 
make any such enquiry. "He eats because the food tastes good 
and makes him want more. If you ask him ichy he should 
want to eat more of what tastes like that, he will probably 
laugh at you. The connection between the savory sensation 
and the act it awakens is for him absolute and selostvei stdnd- 
lich, an a priori synthesis of the most perfect sort, needing no 
proof but its own evidence. To the metaphysician alone can 
such questions occur as: Why do we smile, when pleased, and 
not scowl? Why are we unable to talk to a crowd as we talk 
to a single friend? Why does a particular maiden turn our 
wits so upside down? The common man can only say, '0/ 
course we smile, of course our heart palpitates at the sight of 
a crowd, of course we love the maiden, that beautiful soul clad 
in that perfect form, so palpably and flagrantly made from all 
eternity to be loved!' "i 



i William James, Principles of Psychology, chapter xxiv, pp. 386- 
387. 



2 INTRODUCTION 

Thus we see that not only the mainsprings of behavior, but 
also the moulds which shape and direct our multifarious partic- 
ular activities are, in the end, animal, racial, instinctive. The 
mind is no receptive waxen tablet on which any and every 
element of the physical world can equally impress its sensory 
image. We see and hear only what attracts our attention; we 
notice only what awakens our interest and stimulates, directly 
or indirectly, those dispositions developed in the long course 
of evolution, which we call instincts. In fact, so large a part 
do instinct and habit play in our lives, that it is seriously 
maintained by a great psychologist^ that man seldom reasons 
and that other animals never reason. 

But while the behavior of men is naturally instinctive, it is 
sometimes forced by circumstances to be something more. 
The insects, it is true, live a life almost purely instinctive; but 
then, the problems which they have to face are almost unvary- 
ing, so that one hard and fast chain of instincts can advantage- 
ously direct the honey-comb construction of the Mason bee, 
or the egg-laying activities of the solitary wasp or Yucca moth. 
Our human problems, however, are far too unstable and novel. 
No inherited disposition could keep pace with the enormous 
changes which have come over civilized life within the last 
two generations; and even within the brief span of one gener- 
ation, our habits need to be readjusted and remodeled, again 
and again. There is thus in our lives something more than 
instinct or habit, something continuously readjusting, re-shap- 
ing our ways, forever solving problems forever new, inventive, 
creative — in a word, what we call intelligence, thought, or 
reason. 

How is this done? How does intelligence re-shape our 
lives? How does thought add moral or economic cubits to 
our stature? How does reason enable us to lead lives more 
nearly approaching the ideal? Let us consider briefly some of 
the ways by which we rise above instinct and habit. One of 
these is definition, fixing the meaning of an idea in such a 
way that, amid all the changes and chances of our fluctuating 
experience, we hold fast to that one meaning, that one direc- 
tion of our thought. Another is analysis, the splitting up some 
complex whole into parts so simple that we can readily appre- 
hend their nature, and readily grasp the plan of the whole 

2Wilhelm Wundt. 



LOGICAL ATTITUDE 3 

constructed out of such parts. Yet another is inference or 
reasoning, with all its various forms, by which from a given 
situation we construct mentally the probable consequences or 
antecedents, and generally enlarge our mental horizon and 
Vlear up our ideas. All of these are forms of scientific method, 
the indispensable handmaid of efficiency and success in com- 
merce, in education, and in all the organized institutional 
activities of the present day. 

The logical attitude of mind, then, is concerned with the 
solution of problems, the bridging of gaps,, the removal of 
inconsistencies and inefficiencies, in cases where instinct and 
habit alone would be insufficient. There is none of the "of- 
course-ness" of instinct about this mental attitude. It is 
reasoned, deliberate, thought-out activity. It has also none of 
the warmth and immediacy, and none of the vagueness and 
confusion, of feeling. It is calculating, cool, calm, clear-cut, 
precise; deals little in promises and much in proofs: little 
in speed and much in sureness; hesitates in drawing conclu- 
sions, but succeeds broadly and inevitably in the end; and is 
not without its own vision, its uplifting trust in the final 
rationality of the universe. 

The Study of Logic. — The value of cultivating such a mental 
attitude is beyond question. Without it much of our art and 
all of our science would disappear; the religion of Apollo 
would give way to the worship of Pan; and the reign of Chaos 
Find Old Night would come again. But how to cultivate this 
attitude — by studying logic? This has been, and still is, called 
in question. Plato reasoned sublimely before Aristotle wrote 
the Analytics; and many of our foremost scientists have never 
opened the pages of our logical manuals. And we must con- 
sider a second point: if we study the logic of mathematics, 
does this make us mathematicians — or logicians? If we study 
the logic of the emotions, does this teach us to feel — or to 
reason ourselves out of feeling? If we study the logical 
principles of any subject, does this give us practical mastery 
of the subject — or theoretical mastery of the principles? Com- 
mon sense and a wide experience of men come to the same 
conclusion. It is well known that theoretical masters in the 
field of Pedagogy — men like Kant and Pestalozzi — sometimes 
make poor teachers; and authorities in the field of Aesthetics 
are seldom themselves creative artists. To put it briefly: if 
the attitude comes without studying the theory, and if mastery 



4 INTRODUCTION 

of the theory is consistent with almost total absence of the 
practical attitude, what, if any, is the value of studying logic? 

To this question there are two answers. The first answer 
is given by Hegel, Bosanquet, and many other writers in the 
field of logic. With great modesty they disclaim any practical 
value for their study, and assign to it only that theoretical 
value to which any pure science can lay claim. If we desire 
to know what are the laws of thought, the principles on which 
the validity or correctness of our thinking depend, we have 
as much right to raise such questions as we have to study pure 
physics or pure mathematics. All such studies, like meta- 
physics, have their sufficient justification in that reaching out 
after knowledge as such, which is fundamental in our human 
nature, even apart from practical values. There is a satisfac- 
tion in knowing, quite apart from the question of using our 
knowledge; and many logicians are content to leave on one 
side the question of use, in their certain enjoyment of that 
satisfaction which comes from finding, discovering, knowing. 

It is possible, however, to answer the question differently. 
While it is true that, in its higher branches, logical study is 
somewhat remote from every-day concerns, still, even at its 
deepest, it intensifies and quickens our vision of Truth, and 
justifies, by the insight which it brings, that confidence in the 
intelligibility of things, which is fundamental in the logical 
attitude of mind; and as to its more elementary branches — it 
is merely self-deception if we suppose that there was ever a 
great scientist who was not also a good logician. Every scien- 
tific text-book and every laboratory course lays especial weight 
on questions of method, methods of observation, methods of 
evaluating results, methods of establishing conclusions. But 
these methods are not peculiar to physics or biology as such. 
They belong to the general theory of method, which is a branch 
of logic. Again, the researches of advanced scientists, on 
which so much of the progress of knowledge depends, are 
almost always investigations to test the validity of inferences, 
the theoretical value to be assigned to conclusions, perhaps 
even to the theoretical assumptions underlying scientific rea- 
soning. All these, however, fall within the province of logic. 
The simple truth of the matter is this: a little experience, a 
little common sense, enables each one of us, as we say, to 
reason correctly, whether we have studied technical logic or 
no; and so long as we move only within the more elementary 



STUDY OF LOGIC 5 

reaches of experience, our common sense standards of truth 
are, perhaps, sufficient. But if we wish to raise ourselves 
beyond this elementary and limited sphere; if we wish to 
think clearly and consecutively in order to reach conclusions 
above the level of mere common sense; if we wish to acquire 
business efficiency, or to succeed beyond the average in life 
or in science, we need to withdraw, for a season, from the 
more active concerns of mere living, and reflect carefully and 
systematically on the principles and methods of right thinking. 
Then, having acquired some grasp of the theory beyond what 
the average man knows or suspects, we can apply our deeper 
insight in order to attain a higher level of efficiency and suc- 
cess than is possible without such reflection; and in order to 
cultivate the best fruits of the logical attitude of mind, it is 
necessary to make ourselves thoroughly familiar with the prin- 
ciples and methods of right thinking — in a word, to study 
logical theory. 

Preliminary Definition of Logic. — Logic, then, is the 
study of thought — systematic reflection on the principles 
and methods of right thinking. This statement is cor- 
rect, but is not sufficiently precise to serve as a scientific 
definition of logic. Psychology, for instance, includes a 
study of the thought-processes, and to some extent deals with 
the methods of right thinking. Is logic, then, a branch of 
psychology? If, as its name implies, psychology were studied 
as the general science of mind, or the general science of 
behavior, it would include the study of logical behavior or 
right thinking, and logic would certainly be a department of 
psychological investigation. But in present day practice, 
psychologists tend to regard their science, not as the general 
science of mind or behavior, but as one special mental science; 
and while they do study logical behavior, they do so in a very 
restricted way, and from a view-point entirely different from 
that taken by logic. 

Let us consider an instance. Suppose Mr. A to have recently 
become a member of the Republican party, or of the Congre- 
gational Church. Psychological explanation of this change of 
heart would lay especial emphasis upon the various elements 
in Mr. A's personal history and environment which had led 
him to take the step in question: the influence of old and 
new associations, the weight of social pressure, the greater 
appeal of the new opinions — what he would himself, perhaps, 



6 INTRODUCTION 

call their greater reasonableness. In other words, the view- 
point of psychological explanation is genetic, and traces the 
steps in his personal evolution which gradually led up to the 
change in question. This genetic, historical kind of analysis 
is, however, sharply to be distinguished from logical analysis. 
The logical analysis of this conversion, for instance, would 
consist of a clear setting forth of the arguments pro and con. 
in such a way that we could see the greater comprehensive- 
ness, consistency, and truth of the new opinions. It would be 
concerned, not at all with the historical side of the thought- 
processes as such, but wholly with their meaning, with the 
hanging together of the thoughts in a consistent system, in 
accordance with the standards of truth. Whether reasoning 
is consistent or inconsistent, whether conclusions are true or 
false, no psychology can tell us. Truth and consistency are 
not mere matters of history or personal evolution, but have 
their own standards and laws, and the scientific study of these 
laws is logic. Psychology deals with the process-side, logic 
with the validity-side of thought. 

If, then, we wish to mark out the field of investigation with 
a preliminary definition, we can say: logic is the scientific 
study of the laws or principles on which tne validity of right 
thinking depends: or, more briefly, logic is the study of 
validity. 

FOR FURTHER READING 

A. E. Avery, Tlie Present Day Conception of Logic : Philosophical 
Review, Vol. XXVII, pp. 405-412. B. Bosanquet, Essentials of Logic, 
pp. 1-34. J. Dewey, Essays in Experimental Logic, pp. 1-74. B. Erd- 
mann, Logik, (2nd Edit.), pp. 1-33. E. Husserl, Logische Untersuch- 
ungen, pp. 3-8. H. Lotze, Logic, pp. 1-9. Chr. Sigwart, Logic, pp. 
1-2. W. Wundt, Logik, (3rd Edit.), Vol. I, pp. 1-9. 



PART I 
JUDGMENT i 



1 The word judgment is used in modern logic, in order to emphasise 
sharply the difference between logic — which studies what we think or 
actually judge, i. e., the actual living thought — and grammar, which 
studies the verbal expression of thought. Historically, the two have 
frequently been confused, so that in place of an analysis of the living 
thought, the logician has given a grammatical analysis of the dry 
bones of verbal expression, i. e., of "propositions" or statements, in 
place of judgments or thoughts. 



CHAPTER I 
TYPICAL STAGES OF JUDGMENT. 

The Simple&t Judgments. — In every scientific study, we 
start with the simple and proceed gradually to the complex. 
Logical study also starts with the simple. ■ What, then, is the 
simplest kind of valid thinking, the unit, as it were, of 
thought? Let us consider an example. "If the sun is shining, 
we will go to the woods; but if it is wet, we will stay in and 
read." We have here a single thought. But though single, 
it is obviously not what we should call simple, but is evidently 
complex. Let us analyse it, or split up the complex thought 
into simpler parts. "The sun is shining"; "We will go to 
the woods"; "It is wet"; "We will stay in"; "We will 
read." If we compare each one of these brief statements 
with the original example, we see at once that they are much 
less complex. Let us further compare them with one another. 
"The sun is shining" and "It is wet" appear to belong together, 
to represent two forms of the same kind of judgment. Let 
us regard them as one group, group A. Similarly "We will 
go to the woods," "We will stay in," "We will read," seem 
to express one and the same kind of thought, and thus to 
belong to a "we will" group, which represents a kind of 
thought different from that expressed in group A. Let us call 
the "we will" group, group B. The thoughts in group B are 
judgments of purpose, and seem more complex than judg- 
ments of sense-perception such as "The sun is shining." We 
shall therefore regard group A, i. e.. judgments of sense-per- 
ception, as the simplest kind of judgment revealed by a con- 
sideration of our example. 

Are such perceptual judgments, however, to be considered 
as ultimate? Are they, in fact, the simplest judgments we 
can make? Perhaps we should draw a further distinction. 
"It is wet," for instance, might be thought less complex than 
"The sun is shining." Perhaps the distinction will become 
plainer if we compare "It is fine" with "The sun is shining," 
and "It is wet" with "The rain is heavy." Many logicians 



10 TYPICAL STAGFS OF JUDGMENT 

have, in fact, regarded such impersonal judgments at the 
simplest thoughts we can have.2 It seems better, however, 
to speak of more primitive or less developed forms of the 
same type of judgment, rather than of greater simplicity or 
less complexity. "It is fine" and "The sun is shining" have, 
after all, substantially the same meaning. The only logical 
difference is, that the meaning is more clearly expressed in 
the more developed form. We shall accordingly take as the 
simplest and most elementary acts of thought which we can 
discover, judgments such as "This is red," "It is warm," 
"There is a noise," "This is heavy," "That tastes bitter," 
"There is an odor," etc. — i. e., simple judgments of sense- 
perception. 

The Elements of Judgment. — In the above instances we have 
judgments so simple, that here, if anywhere, we should be 
able to pick out some of the elements upon which the validity 
of judgments depends. In cases which were more complex 
we might be unable to see our way. But in these simple 
cases, if anywhere, we should be able to discover at least the 
more obvious elements. Let us therefore consider these judg- 
ments of perception closely. Can we discover any simple fac- 
tors, any constituent elements of such judgments? 

Two elements, upon which perhaps the validity of judgment 
depends, we can discover almost at once. These elements are 
(a) sensory, and (b) intellectual, (a) All judgments of per- 
ception are thoughts about something present, something given 
to us in perception, given to us through the senses, sensory. 
"This-red," "Warm-feeling," "Noise-here," "That-bitter-taste," 
etc. It may be that all judgments whatever, and not merely 
perceptual judgments, are similarly thoughts about something 
which is, in the end, given to us in sensation. In this case, 
all thought would have this sensory element, and the func- 
tion of sensation would be, to furnish us with a channel by 
means of which we could come to know objects, or things- 
which-we-can-experience. (b) On the other hand, so far as 
judgments of perception are thoughts about something pres- 
ent, they undoubtedly contain an element which we should 
call intellectual. This is in such cases, not so easily noticed 
as is the sensory element. In order, then, to bring out more 



2 For a recent study of the whole subject of the impersonal judg- 
ment, see S. F. MacLennan, The Impersonal Judgment, 1897. 



ELEMENTS OF JUDGMENT 11 

clearly the presence of the intellectual element, we shall pro- 
ceed to take a number of slightly more developed cases of per- 
ceptual judgment. "This paper is red," "It is warm near the 
stove," "There is a noise at the door," "This oook is heavy." 
These instances are all perceptual, but we can at once observe 
that certain intellectual elements are now more prominent. 
Instead of reference to the undifferentiated "this" as the 
sensory given, we refer to the paper, stove, door, book, etc., 
i. e., to determinate objects, the recognition of which involves 
distinction, comparison, classification, etc., which are proc- 
esses predominantly intellectual. Let us. further consider yet 
more developed perceptions. "This paper is a brighter red 
than that," "It is warmer near the stove than near the door," 
"This book is heavier than that." We have here much the 
same general sensory elements as before. But we now have 
in a very clear and explicit form the intellectual act of 
comparison. "This paper" and "That paper" are held 
together in one intellectual act, and are compared in 
respect of their brightness-value. So too "Near the stove" 
and "Near the door" in respect of their warmth. In fact, the 
more highly developed such judgments become, the more 
plainly can we observe the presence of intellectual elements. 
But in the very elementary and primitive cases too we can 
now see the presence of abstraction and recognition at least. 
The "This" is differentiated into red, warm, heavy, etc., and 
these are not only clearly apprehended, but are apprehended 
in distinction from one another. In other words, in these 
simplest of all judgments there is present, not only a sensory, 
but also an intellectual element. 

Typical Stages of Judgment. — With the sensory element in 
judgment, logic is not, as a rule, much concerned. It is in 
epistemology or the theory of knowledge, that the function 
of sensation as a factor in knowledge is especially studied, and 
it is still a question whether the theory of knowledge should 
or should not be regarded as constituting an integral part of 
modern logical investigation. 3 We shall therefore postpone, 
for the moment, further discussion of the sensory factor in 

3 Schuppe (ErkenntwtetheoretisLche Logil'J, Wundt. and YTindelband 
(Encyclopadie der philosophischen Wissenschaften. Vol. I) regard the 
theory of knowledge as falling within the field of' logic, or vice versa. 
Erdmann incorporates "corollaries" from the theory, of knowledge in 
his logical Element arlehre. Bradley and Bosanquet are also to be 
reckoned among the epistemological logicians. 



12 TYPICAL STAGES OF JUDGMENT 

judgment, and shall consider more closely the intellectual 
factor. 

In order, however, to deal with the intellectual element in 
judgment in any adequate way, we can certainly not confine 
ourselves to elementary perceptual judgments. It is no longer 
a question of picking out the least complex type of judgment 
in order to avoid obscurity, and in order to enable our unac- 
customed eyes to see their way in a simple case. We have 
now to face the more general problem of validity in judging 
as such, and this involves consideration, not only of the ele- 
mentary cases, but also of the more highly developed forms 
or stages of judgment, in order that nothing vital may be 
overlooked. In order, then, to clear the way for our whole 
subsequent investigation into the sensory and intellectual 
factors, we must be able to cover, in some clear and brief 
way, the whole field of judgment. This we shall do by arrang- 
ing different kinds or stages of judgment in a table, starting 
with the more elementary and proceeding to the more 
advanced — i. e., proceeding from judgments in which the intel- 
lectual element is less prominent to cases in which it is more 
prominent. 

TABLE OF JUDGMENTS 

L Judgments of Perception. — E. g., "This room is warm," 
"This oak has less foliage than that beech." 

2. Judgments of Experience, — E. g., "The freight-trains 
passing over the bridge grow more troublesome every year," 
"Noise is usually a compound of tones." 

3. Symbolic Judgments. — E. g., "Rome was occupied by 
Caesar," "Strathcona lies on the North Saskatchewan," (where 
the evidence is not direct experience, but a textbook account 
of a place we have never seen). So too "The theory of the 
synapse is fundamental for the explanation of conscious 
behavior" (where we have had no direct experience of syn- 
apses). 

4. Transcendent Judgments. — E. g., "God is a substance 
consisting in infinite attributes, of which each expresses 
eternal and infinite essentiality," "Things-in-themselves are 
absolutely unknowable," "True evolution is the progressive 
self-organization of a system of timeless selves." 

Let us explain briefly the above distinctions. A judgment 



TYPICAL STAGES OF JUDGMENT 13 

of experience differs from a perceptual judgment, in that it 
depends more on memory of previous perceptions than on 
direct present perception. It is more developed, and sums 
up many previous experiences, as a composite photograph 
gives us the result of many direct likenesses of actual per- 
sons. For instance, "Most writing-paper is white" sums up 
many experiences of writing-paper, and while on the one hand 
less direct and immediate than "This writing-paper before me 
is white," on the other is more advanced, more representative, 
more intellectual, than the simple perceptual judgment. Still, 
even in the perceptual judgment there is some appeal to pre- 
vious experiences. For we know the object before us to be 
"writing-paper" and "white." The distinction between judg- 
ment of perception and judgment of experience is thus not 
absolute, but is a question of more or less, a matter of degree. 
Where the sensory element predominates, we have the stage 
of judgment which we call judgment of perception. Where 
the intellectual element plays the greater part, we have the 
judgment of experience. 

A symbolic judgment differs from a judgment of experience, 
in that we are here dealing with a sort of extension of our 
experience, based indeed on previous experiences, but con- 
structing, on the analogy of these past experiences, new objects 
of similar type, objects which we might possibly have experi- 
enced, or might possibly experience in the future, but which 
in actual fact we have never experienced. Thus, if we had 
lived in Rome at the time of its occupation by Caesar, our 
thought would be a judgment of experience, if not, indeed, a 
perceptual judgment. But where we have had direct experi- 
ence of cities differing from Rome, and can only construct 
for ourselves imperfectly, in the light of very inadequate past 
experience, what it meant for a city to be occupied in war- 
time by the forces of Caesar, our judgment is only symbolical. 
The less directly the case happens to be related to our per- 
sonal experience, the harder do we find it to spread out our 
experience so as to make vivid to ourselves scenes so remote 
from what we have seen and felt, and the further do we tend 
to fall short of full realisation of the meaning of our judg- 
ment. We have the bare skeleton of experience. The flesh 
and blood, the living elements, are almost totally missing. In 
such judgments, while the sensory element may be weak, the 
intellectual element of construction is far more prominent 



14 TYPICAL STAGES OF JUDGMENT 

than in judgments which remain contentedly within the 
circle of our own experience. And yet, in judgments of experi- 
ence also there is some construction, some putting together 
of past experiences in order to produce something new, the 
composite result which — as a composite unity, at any rate — 
was never actually experienced. We see then that here also 
the difference is a question of more and less, a matter of degree 
only. Where the sensory element is relatively greater and 
the intellectual construction relatively less, we have a judg- 
ment of experience. Where the constructive, intellectual 
element decidedly predominates, we have the symbolic judg- 
ment. 

The transcendent judgment differs from the symbolic judg- 
ment, in that v/e here transcend or go beyond, not merely 
our actual experiences, but also even possible human experi- 
ence. In the symbolic judgment, our subject is always some- 
thing which might conceivably be experienced, or have been 
experienced. But in the transcendent judgment, the subject 
could never be experienced. Where, for example, our experi- 
ence is finite, any judgment about the infinite transcends the 
possibility of experience, and we have a transcendent judg- 
ment. Such judgments are both natural and common. How 
natural, or rather inevitable, any attempt to think one's way 
to a first cause, or to a profound and satisfying standpoint for 
the conduct of life will show. How common, the slightest 
reflection on human mental history will sufficiently attest. 
Consider, for example, the ever recurring interest in mysti- 
cism, the medieval search for the philosopher's stone, the 
inventor's fascination in the case of perpetual motion, the- 
still not uncommon belief that one can read destiny by the 
lines in the palm of the hand, if not by the conjunctions of 
the heavenly bodies. The "anticipations" of scientists — 
intended, no doubt, as symbolic extensions of experience — 
teem with transcendent judgments. Most of our philosophi- 
cal theories, much of our moralising, and much of our relig- 
ious thought is transcendent. In every walk of life the human 
yearning after some ineffable ideal, some unspeakable perfec- 
tion — the "vision" (as we call it) of ideal truth, power, love, 
or happiness — leads us insensibly and inevitably beyond the 
narrow confines of possible experience. 

While in strict theory it might seem as though transcen- 
dent judgments were sharply distinguished from symbolic judg- 



TYPICAL STAGES OF JUDGMENT 15 

• 
ments, in definite cases the line cannot be drawn with pre- 
cision. Transcendent judgments contain some sensory and 
experiential elements, and symbolic judgments contain a fair 
portion of that idealising tendency which frees the imagina- 
tion from the fetters of actual experience. A transcendent 
judgment is thus only an exaggerated symbolic judgment, and 
the distinction, here also, is one of more and less. Where the 
idealising tendency, the intellectual element, is more 
restrained, we have a symbolic judgment. Where it is almost 
wholly loosed from its experiential moorings, where the sen- 
sory element is distinctly less prominent, we have the tran- 
scendent judgment. 

The above stages cover the whole field of human thought. 
They represent four stages of judgment, distinguished from 
one another only relatively, according as the perceptual or 
the intellectual element predominates. The simplest judg- 
ments of perception exemplify, to some extent, the operation 
of the elaborative, idealising tendency of intellect. And the 
most transcendent judgments we can make, the finest thought- 
webs we can spin, are still attached to earth by some sensory 
threads, gilded o'er by the warmth of personal feeling and 
personal sense-experience. A pure intellect and a pure sen- 
sation are equally beyond our human thought. All our think- 
ing moves within these two extremes, and partakes of both 
principles in varying proportions. It may be that some prin- 
ciple yet more profound remains to be discovered. But the 
presence of these two principles — in perceptual, experiential, 
symbolic, and transcendent judgments alike — is certain, and 
for the present we must look for the conditions, on which 
the validity of all judgment depends, in the sensory and intel- 
lectual elements. 

FOR FURTHER READING 

J. E. Creighton, An Introductory Logic, chapter xxiii. J. Dewey, 
Essays in Experimental Logic, pp. 183-219. B. Erdmann, Logik, (2nd 
Edit.), pp. 426-429. R. C. Lodge, The Division of Judgments: Jour- 
nal of Philosophy, etc.. Vol. XV, pp. 541-550. 

EXERCISES 

1. Try whether you can discover any judgments simpler than judg- 
ments of perception. For instance, are any of the following more 
simple than perceptual judgments : Remarkable ! Fire ! Good ! 
Thieves ! Dinner ! 



16 TYPICAL STAGES OF JUDGMENT 

2. Can you think of any judgments which cannot be classed as 
perceptual, experiential, symbolic, or transcendent — or at least some 
transition-form of these? Try to classify the following, arranging 
them under separate heads, as (1) perceptual, (2) experiential, (3) 
symbolic, (4) transcendent: Up we go! It takes thirteen days to 
get from here to Paris. Everywhere you see grain elevators. Nero 
fiddled while Rome was burning. The prince now possessed the magic 
sword, the cap of darkness, and the seven-league boots. I am the 
master of my fate, I am the captain of my soul ! This color-mixture 
of yellow and blue gives gray. A thick rug under the feet tends to 
prevent chilblains. You can buy a* good boat for $40.00. Humpty 
Dumpty sat on a wall. Seven plus five equals twelve. O king, live 
for ever ! The hens are laying more eggs than ever before. You are 
looking pale. These weeds are choking the vegetables. It is sure to 
rain on Thanksgiving Day. 

3. Go over your classified list of the judgments given in the pre- 
ceding exercise. Can some of the experiential judgments be regarded 
as perceptual? Can some of the symbolic judgments be regarded as 
experiential? Can some of the transcendent judgments be regarded 
as symbolic? And is there an experiential element even in judgments 
of perception? Is there a symbolic element even in the judgments of 
experience? Is there a transcendent element in the symbolic judg- 
ments? Do all the forms pass into each other by easy, and almost 
imperceptible, gradations? 



CHAPTER II 
THE SENSORY ELEMENT IN JUDGMENT. 

The Sensory Element. — In order to study the sensory ele- 
ment in judgment, it would, perhaps, be convenient if we could 
isolate it and examine it in a separate case, uncontaminated 
by any admixture of foreign elements. But, as we have seen, 
the sensory element is never found alone; no judgment is 
found in which the sensory elements are not shot through 
and through with intelligence, organised and built up into 
something more than mere blind sensation. The most that 
we can do, if we wish to discover the validity-value of sensa- 
tion, is to consider a variety of cases, neglecting the intel- 
lectual element, and concentrating our mental microscope on 
the part played by sensation in giving us a judgment on whose 
validity we can rely. In order that the cases considered shall 
cover the whole field of thought, we shall make use of the 
table of judgments established in the last chapter, and shall 
begin with judgments of perception. 

(A) In Judgments of Perception. — What is the sensory ele» 
ment in simple judgments like "This is warm/' "This is 
green," "This is hard," "This is heavy," etc.? On the one 
hand we have a reference to the general sensory continuum 
which furnishes the background and setting for our more 
highly specialized experiences; and on the other, in the 
"warm," "green," "hard," etc., we have the attribution of a 
special sensory quality, in this setting, to some object ("this") 
singled out for particular notice. The abstraction which 
singles out a particular quality from the general sensory set- 
ting, is, no doubt, intellectual: it is a mode of articulation or 
organisation of the sensory side of experience. What remains 
as the definitely sensory element is (1) the unspecialised feel- 
ing of bodily existence. This is composed of the memories, 
associations, sensations, etc., which together constitute the 
background of the consciousness of John Smith, as distinct 
from that of Henry Jones, etc. We carry this feeling of our- 
selves about with us: it prejudices us in various ways, colors 

17 



18 SENSORY ELEMENT IN JUDGMENT 

all our thoughts, and spreads itself unnoticed over all our ex- 
periences. It is more than merely sensory, but a large part of 
it is definitely sensory, and requires consideration, as underly- 
ing every judgment we make. (2) A further sensory element, 
differing with different judgments, is that by which we dis- 
tinguish "warm" from "green," etc., i. e., not the distinguish- 
ing itself, which is intellectual, but the positive quality in each, 
by which we experience warmth as warmth, as the specialised 
mental reaction to a temperature-stimulus, and green as green, 
the specialised color-consciousness, etc., i. e., the positive 
quality of the special sensation, in virtue of which one sensa- 
tion can be distinguished from another. This specialised 
sense-experience is ultimate, and can not be explained except 
by reference to the conditions of its appearance in conscious- 
ness. It has to be experienced to be appreciated as warmth, 
green-ness, etc., and constitutes the specialised sensory element 
in simple judgments of perception. 

(B) In Judgments of Experience. — What is the sensory ele- 
ment in such judgments as "The freight trains crossing the 
bridge grow more troublesome every year"? What is espe- 
cially present to sense is ex nypothesi no more than a low 
rumble, which is interpreted as due to a distant freight train; 
by association former instances of such trains are recalled, 
and a comparative judgment, based upon such experiences 
and summing up their result, comes to be formed. That is to 
say, the actually present sensory element is (1) the general 
feeling of bodily existence already noticed in the case of per- 
ceptual judgments, and (2) the special complex of sense-qual- 
ities which constitutes a "rumble." So far there is not much 
difference from what we found in the perceptual judgment; 
but in judgments of experience, the weight of the judgment 
rests less on the actually present sensory elements noted 
above, and more on the recalled, reinstated, ideally present 
sensory experiences of the past — i. e., less on the present sen- 
sation, and more on its fringe of associations. So too of the 
inductive generalisations of science, exemplified in such judg- 
ments as "All noise is a compound of tones." This represents 
a summing up of past experiences, and the occasion for mak- 
ing such a judgment of experience is, no doubt, some present 
instance of "noise" or "tone." The judgment of perception 
thus rests more immediately on what is present, the judg- 
ment of experience more mediately on the given sensation; 



SYMBOLIC JUDGMENTS 19 

but in both cases the sensory element consists of (1) the gen- 
eral background, and (2) a special stimulus which stands out 
from that background. 

(C) In Symbolic Judgments. — In judgments such as "Rome 
was occupied by Caesar," the reference is, of course, to an 
experience into which we do not enter immediately. We 
reconstruct for ourselves in idea, so far as our own experience 
furnishes us with analogous elements, an experience which 
was never actually ours. What is the sensory element in such 
judgments? There is certainly present (1) the actually given 
sensory continuum, the sense of bodily existence which spreads 
itself over our reconstructions and clothes the dry bones of 
narrative with our flesh and blood, fusing the living present 
with a merely imaginary past, so that we can say indiffer- 
ently, either that we are transported bodily into the past, or 
that the past is made to live again in the present. In addi- 
tion to this general sensory element, there is also present (2) 
some special stimulus which directs our thoughts to the past, 
to Rome for instance rather than to Athens, and to Caesar 
rather than to Pompey. Such stimulus is furnished as a rule, 
either by reading or hearing something about Rome or Caesar, 
or at least something which by association awakens thoughts 
of Caesar and Rome. The special sensation — e. g., of visual 
or auditory signs of words — is here somewhat more remote 
from the reconstructed experience than we found to be the 
case in experiential judgments, while the general sensory set- 
ting seems to play a relatively greater part, but in the sym- 
bolic judgment also the sensory element consists of (1) the 
general background, and (2) some special stimulus arising 
against that background. 

(D) In Transcendent Judgments. — In judgments such as 
"God is a substance consisting in infinite attributes," or 
"Things-in-themselves are absolutely unknowable," i. e., in 
judgments concerning entities which could never be objects of 
sense-experience, it seems at first sight as though there could 
be no question of sensation, as though such judgments must 
be the product of pure thought, unmixed with any element 
from the sensory side of our nature. And yet, let us consider. 
The first judgment has meaning for Spinoza's readers, pre- 
cisely because two of the Divine attributes are definitely 
known. These are "extension" and "thought," the "essence" 
of body and mind, much as we experience body and mind. It 



20 SENSORY ELEMENT IN JUDGMENT 

is when we extend the attributes of Deity so as to include not 
only the two which we do experience, but also an infinity of 
others of which we are unable to form the slightest idea, that 
we realise the transcendent nature of the judgment. As far 
as we remain within human experience, so far we feel sure 
of our ground, so far the judgment has positive significance 
for us; the "infinity" of divine attributes would be utterly 
meaningless for us if we were not already acquainted with 
two of them, and could thus regard the rest as a kind of 
extension, by analogy, of our experience, could attempt to 
spread out this experience so as to cover, however thinly, the 
infinite. So far, however, as the judgment is strictly tran- 
scendent, so far as it deals with an infinity of attributes 
which we cannot conceive, cannot think positively, so far 
we are attempting to conceive the inconceivable and judge 
the unjudgeable. In other words, the transcendent judgment, 
natural and common as it is, really represents a failure to 
judge. Imagination takes the place of strict thought, and 
feeling — often, no doubt, sublime, but still, always merely sub- 
jective — usurps the place of critical reason. 

These observations, however, do not solve our present prob- 
lem. Because sense-experience is inadequate to extend itself 
over the infinite, it does not follow that the attempt is not 
actually made. In every judgment, however transcendent, 
there is, in fact, always present (1) the general sensory set- 
ting of our experience, which colors alt our actual thinking, 
and projects itself to distant spaces and times to cover all 
objects of our present thinking, such as Rome, Caesar, the 
synapse, God — and in virtue of so staging them against the 
sensory background of our own experience, so colors them 
that they become ours, parts of our intimate self-conscious 
experience, here and now. However inadequate this extension 
may be in the case of transcendent, metaphysical entities, still, 
so far as we concern ourselves with them, we think of them 
in sensuous images, in radiations outward from our present 
center of sense-experience. Again (2), there is always present 
some special sensory stimulus which directs our thought into 
paths which lead beyond the knowable. Usually indirect, as in 
the case of the written or spoken symbols which furnish the 
starting-point for symbolic judgment, there is no element in 
sense-experience which is unable to guide us into thoughts 
which do often lie too deep for words. Our life rests always 



TRANSCENDENT JUDGMENTS 21 

upon a vast ocean of unsolved questionings, and any chance 
sensory stimulus may suffice to plunge us into the abysses of 
that ocean. Thus we see that in transcendent judgments also 
the sensory element consists of (1) the general background 
to which we have so frequently referred, and (2) a special 
stimulus arising against that background. 

Summary. — If we now cast our eyes over the whole field of 
judgment, we notice that while in every case there is present 
a general and a special sensory element, these are present in 
varying proportions. As we pass from perceptual judgments, in 
which the intellectual element is relatively less important, to 
judgments in which the sensory element is slight and the 
intellectual interpretation almost everything, we observe that 
the general sensory background of experience plays an increas- 
ingly greater part. On the other hand, the special sensory 
stimulus, so vital in judgments of perception, becomes dwarfed 
into relative insignificance in the case of transcendent judg- 
ments. The stimulus, e. g., of a red surface, which is so all- 
important for the perceptual judgment "This is red," is of 
importance for the experiential judgment less as an ultimate 
sensory quality, and more on account of the associations which 
it calls to mind. In the symbolic judgment, where the asso- 
ciations are more remote, its direct sensory quality is still less 
important, and finally, in the transcendent judgment, it is 
almost a chance affair, almost a matter of indifference: for all 
roads lead alike to the obstinate questionings which underlie 
and perplex our whole life. Great, however, as are these 
variations, in every judgment we find present both general 
and special elements of a sensory kind. 

FOR FURTHER READING 

W. James, Principles of Psychology, Vol. II, chapter xvii. H. Lotze, 
Logic, sect. 2. A. Riehl, Der philosophische Kriticismus, Vol. II, 
chapter i. G. F. Stout, Manual of Psychology, Bk. II, chapters Mi. 
Proceedings of the Aristotelian Society, N. S., Vol. VI, pp. 360-362 
(quoted in B. Gibson, The Proolem of Logic, pp. 82-84). W. Wundt, 
Logik, (3rd Edit.), Vol. I, pp. 10-69. 

EXERCISES 

1. What precisely are the sensory elements in : Here comes Mr. 
Smith. This bread tastes excellent. I am taller than you? 

2. What precisely are the sensory elements in : Electricity is much 
more efficient than gas. Such requests for subscriptions always sue- 



22 SENSORY ELEMENT IN JUDGMENT 

ceed. Eggs placed in water-glass keep for several months. I am 
always nervous before a large audience? 

3. What precisely are the sensory elements in : Not more than 
three men in a thousand would vote for that program. At least fifty 
per cent of actions called criminal are due to our social system. For 
a small house, you will find hot water heating the most satisfactory? 

4. What precisely are the sensory elements in : God moves in a 
mysterious way, His wonders to perform. Time and space are unreal 
forms of sense, and disguise the Real. I want to be a great Artist. 
I listened to the language of the birds ; I knew what the trees whisper 
to each other? 

5. Read Henry James: The Soft Side, pp. 8-9, 18-21, and sum- 
marise the essential nature of sensory experience, as there described. 



CHAPTER III 
VALIDITY AND THE SENSORY ELEMENT. 

The Question Concerning Validity. — In the last chapter we 
have described the sensory element. We have treated it as a 
fact, as a constituent part of every judgment, and have stated 
what it is, what we find it to be. All this, however, is merely 
preliminary to a further question, which is the essential ques- 
tion for logic. It remains to ask, not what the fact is, but 
— what is the value of the fact? Being what we have found it 
to be, does this universally present sensory element in any 
way contribute to the validity of judgment? Do the correct- 
ness, certainty, reliability, truth of the perception of warmth, 
redness, etc., depend on our bodily senses? Are we to regard 
sense-perception, the sensory element in judgment, as trust- 
worthy per se, or as untrustworthy — or is it possibly indif- 
ferent? Is. our sense of warmth, for example, perhaps merely 
a de facto condition, a transient event in our embodied expe- 
rience without which we should not judge a given object to 
be warm — a mere happening and nothing more — and do we 
have to look elsewhere for de jure conditions, criteria which 
really test the correctness and trustworthiness of the judg- 
ment?! Are truth and certainty entirely an affair of "intel- 
lect," or do our bodily senses themselves contribute something 
by which the validity of judgments can be tested and 
approved? 

(A) In Judgments of Perception. — In judgments such as 
"This room is warm," there is no doubt that our bodily senses 
play a great part. But the present enquiry is whether this 
part which they play is altogether reliable and trustworthy — 
more particularly, whether any attempt to justify such judg- 
ments inevitably ends in an appeal to sensory experience as 
such. Let us consider. Suppose I feel doubtful as to whether 
the room is warm after all. I can either (1) repeat my judg- 
ment, i. e., give myself up to the sensory feeling, and assure 

i Cf. Wundt, Logik, Vol. I, p. 80. 

23 



Z4 VALIDITY AND THE SENSORY ELEMENT 

myself, by yielding completely to its guidance, that the room 
certainly does feel warm, or at least feels warm to me. This, 
in fact, is our usual procedure in testing perceptual judg- 
ments. That is to say, we accept as trustworthy the sensory 
element as such, and only doubt whether we really had 
allowed it full play, or whether we perhaps were inattentive 
on the previous occasion. If the second experiment confirms 
the first judgment, we are usually satisfied, and enquire no 
further. If, however, our judgment is challenged by someone 
else, or if we have reason to suspect that perhaps our senses 
are deranged, as by a fever, — in which case we may feel warm, 
although the temperature of the room may, in fact, be low — 
in such cases we usually appeal to a thermometer, or some 
similar objective measure, which represents changes of tem- 
perature in a way that appeals, at least immediately, to some 
sense other than that of warmth, e. g., to the eye. This also, 
we must notice, is an appeal to sense-experience, and in actual 
fact, if hard pressed, we are driven to the conclusion that, 
whatever the thermometer may or may not state, whatever 
the temperature of the room may or may not be, we feel warm. 
We feel what we feel, and cannot be argued out of our feeling 
by any reasonings drawn from the reading on the thermom- 
eter, etc. It is a matter of sensory feeling, and not of rea- 
soning. In other words, our conclusion is, that the sensory 
element in the judgment is our own feeling of warmth, and 
if our judgment that the room is warm turns out to be false, 
the falsity depends not on the sensory element, which is what 
it is independently of reasonings about it, but on the intel- 
lectual element which, given the feeling of warmth, interprets 
this experience as due to the temperature of the room. The 
same is the case with all the "illusions of sense" produced by 
mirrors, prisms, or cunningly devised appeals to misleading 
associations. The error depends in all such cases upon some 
misinterpretation which leads us away from the direct appre- 
hension of the sensory elements. Where we are not so led 
astray, where we directly apprehend those elements, the sim- 
ple sensory experiences are, as we have seen, "ultimate." In 
perceptual judgments, all that we can do to test their validity 
is, avoiding interpretations and associations as far as possi- 
ble, to analyse the given case and break it up into parts so 
simple, that an unbiased appeal to sensory apprehension can 
be made, and then — trust absolutely to our direct apprehen- 



IN EXPERIENTIAL JUDGMENTS 25 

sion of the sensory elements. Direct, simple, sensory appre- 
hension thus furnishes the ultimate basis for testing and 
approving the validity of judgments of perception. 

(B) In Judgments of Experience. — In perceptual judgments 
it is, after all, not difficult to see that the sensory element 
must condition the validity of our thinking. We have merely 
to free ourselves from misleading interpretations and asso- 
ciations, and make an unbiased sensory judgment. But in 
judgments of experience the element of interpretation seems 
more essential. Such judgments represent a summing up of 
sensory experiences, and the associations are vital to the con- 
clusion. Here, at any rate, there can be no question of "free- 
ing ourselves from interpretations and associations''; for this 
would be to deprive us of the experiential judgment altogether. 
When, for instance, on the sensory basis of a low rumble, I 
interpret my experience as due to a freight train crossing the 
bridge, surely the case is parallel to the interpretation of a 
feeling of warmth as due to the temperature of the room; and 
when I further compare the disturbance due to freight trains 
in recent years with the similar experiences of the past, my 
judgment is surely based, at least in large part, on associa- 
tions rather than directly apprehended sensations. Judgments 
of experience are thus more complex, and seem to require a 
different kind of explanation. And yet, if we wish to dis- 
cover whether the sensory element here also is a conditioning 
factor in determining the validity of the judgments in ques- 
tion, we must ask, precisely as we did before, whether the 
attempt to justify such judgments inevitably ends in an appeal 
to sensory experience. 

Let us consider. If such a judgment were challenged, how 
should we attempt to justify it? If it were doubted, for 
instance, whether the rumble was really due to a train, we 
should justify our statement by leading the doubter to the rail- 
way bridge, and letting him see as well as hear the train. We 
should then withdraw him gradually from the bridge, until he 
sufficiently realised that the roar of the train gradually 
changed into the low rumble in proportion as he drew further 
away from the bridge. This gradual transition would assure 
him of the continuity of the sensory experience, and he would 
come to see that what in the distance was a rumble was in 
fact one with what was experienced as a "roar of the train" 
in the neighborhood of the bridge. In other words, the proof 



26 VALIDITY AND THE SENSORY ELEMENT 

of the validity of our judgment consists in an appeal to actual 
sensory experience. In this proof we show that the rumble 
sensation is continuous with, and in fact is, the sense-percep- 
tion of a distant-train-crossing-bridge. The intellectual ele- 
ment consists chiefly in so ordering the experience that the 
doubter could give himself up to the sensory side of the expe- 
rience, and realise for himself its thorough-going continuity. 
This appeal to unbiased sensory experience is accepted as final. 

"Yes," it might be objected, "but this is, after all, a per- 
ceptual judgment. You have an auditory perception of a dis- 
tant train. This is a little more elaborate than the percep- 
tion of bodily warmth, but in the last analysis is much the 
same kind of judgment, and in such judgments we have already 
granted that the ultimate appeal is to sense-experience. But 
how about a judgment in which the reference is not to pre- 
sent perception, but to the distant past? How could we justify 
such a thought as that the freight trains in recent years are, 
on the whole, more troublesome than the freight trains in the 
remoter past?" — Well, we answer, how do we justify such 
judgments? The usual method is to appeal to the memory of 
a number of the local inhabitants who have experienced the 
disturbance in question during a sufficient period of years. 
If their conclusions agree with ours, reasonable doubt is 
usually satisfied. In what, then, does this justification by 
appeal to memory consist? It is necessary to inquire, for the 
appeal to memory is certainly an appeal to associations, and 
associations, as we have already seen, are not always to be 
trusted. What, then, constitutes the essential difference 
between a trustworthy recollection, and an association which 
we cannot trust? 

Let us compare the former case — in which uncertainty as 
to the distant train is removed by our realising the spatial 
continuity of (1) the rumble and (2) the train-actually-seen- 
on-the-bridge. In that case, the validity of our judgment 
rested on the spatial continuity of our sensory experience; the 
experience of the "rumble" actually was an experience of the 
spatially distant train. In the present case, can we show that 
the rumble-experience is actually an experience of trains dis- 
tant in time rather than in space? In other words, does our 
sensory experience possess not merely spatial, but also tem- 
poral continuity? Let us examine this. The actual sensory 
present, according to psychologists, embraces a period of time 



IN EXPERIENTIAL JUDGMENTS 27 

covering approximately from two to four seconds. Our sen- 
sory consciousness is at its best at this brightly illuminated 
focal point, and it is what is brought into the center of focus 
that we apprehend most clearly. But our sensory conscious- 
ness has also a margin, and from the brightness of the focal 
center to the darkness of the extreme margin there is unbroken 
continuity, a twilight which deepens by imperceptible grada- 
tions. So it is with memory, with our associations. The 
nearer they are to the present, the more closely connected with, 
the focus of sensory experience, the more clearly can we appre- 
hend their value. They are always continuous, in the stream 
of consciousness, with present sensation. What makes us trust 
the memories of yesterday, and mistrust the memories of 
many years ago, is not absence of continuity, but some diffi- 
culty in so ordering our mental vision that we can directly 
apprehend that continuity. Where we leap to conclusions with- 
out establishing that direct apprehension, we have untrust- 
worthy, uncritically accepted, associations. In order to test 
critically the trustworthiness of memory, we experiment with 
our associations until we are in a position to apprehend 
directly, without bias, and in the present, some sensory ele- 
ment which extends with clearly unbroken continuity into 
the past. In such cases, just as the rumble-sensation is 
directly continuous with the spatially distant train-roar of 
two seconds ago, so also it is directly continuous with the tem- 
porally distant train-roar of ten years ago. In other words, 
the justification, in both cases, depends on establishing clearly 
the continuity of the sensory experience in space and time, 
in such a way that we directly apprehend the distant (whether 
in space or in time) as an extension, towards the margin, of 
the present focal sensory consciousness. 

Finally, in the case of the inductive generalisations of 
empirical science, such as "All noise is a compound of tones," 
justification — or, as it is termed in science, "verification" — 
consists in an appeal to "demonstration," i. e., to the direct 
sensory experience of a typical case. Thus we see that the 
judgment of experience is merely a complex and elaborate 
case of the judgment of perception, and, like the perceptual 
judgments examined previously, is dependent, for its validity, 
upon a direct apprehension of the sensory element. The asso- 
ciations which are misleading, and the interpretations which 
withdraw our attention from this sensory apprehension, must 



28 VALIDITY AND THE SENSORY ELEMENT 

first be removed; we can then realise the full force of the 
sensory elements, with their spatial and temporal continuity, 
and see how they underlie and make verifiable the judgments 
of experience. 

(C) In Symbolic Judgments. — Based as it is on direct past 
experience, it is fairly intelligible that the experiential judg- 
ment can be verified in an extended perception, which fuses 
together past and present in a living unity. It is in fact an 
extended perceptual judgment. But when we come to the 
symbolic judgment, a striking difference seems to confront us. 
In the symbolic judgment we attempt to reconstruct, not a 
distant experience of our own, but — an experience which was 
never ours, an experience which may have belonged to some- 
one else in the past, or may some day come to us — or to some- 
one else — in the future. Surely in such cases there can be no 
question of extending some ray of focal illumination into the 
marginal twilight of our own consciousness — surely here there 
can be no resting upon the living continuity of our own sen- 
sory experience. In studying, for instance, the history of 
Rome, we note its occupation by Caesar. Except metaphoric- 
ally, we cannot, of course, transport ourselves into the first 
century before Christ, and consequently there can be no ques- 
tion of "apprehending directly one continuous experience" 
which extends back to the occupation of Rome in one complex 
perceptual judgment. It would seem, then, that symbolic 
judgments require a different kind of explanation, a different 
kind of answer to the question which, here again, we must 
ask: — In attempting to justify such judgments, do we inevit- 
ably appeal, in the end, to sensory experience? 

It must at once be admitted that no personal experience can 
possibly assure us of the certainty and truth of events which 
lie beyond that experience. What Caesar did when he entered 
Rome, we do not exactly know; as we should say, we were 
not there to see. Accordingly we have to trust to tradition 
rather than to personal experience, and to indirect, in place 
of direct, evidence. Furthermore, familiarity with the errors 
of history books, as well as with works of professed fiction, 
will convince us that we can not infer with certainty from the 
printed statement to the actual occurrence of events. The 
ceytainty and truth, then, of symbolic judgments is and must 
be, in the nature of the case, largely a matter of interpreta- 
tion, of intellectual rather than sensory elements. In this 



IN SYMBOLIC JUDGMENTS 29 

respect, symbolic judgments resemble the perceptual judg- 
ment "It is warm in the room" ; i. e., the immediate sensory- 
element is something less than the total judgment, to which 
intellectual elements also have contributed their part. As in 
the percepiual judgment, in examining into its validity we 
abstracted from intellectual elements, and laid bare the sen- 
sory element in order to apprehend it directly in its full force, 
so here in the symbolic judgment, let us, for the present, leave 
out of consideration the intellectual, interpretative element, 
and try to discover what the sensory element is, and what 
part it plays in the something less than the total judgment.2 
If, then, we leave out of consideration the question as to 
whether, in actual fact, Caesar did or did not occupy Rome 
in the manner indicated by our history book, what remains of 
the complex judgment? There remain two parts which we 
still think: — (1) we still think that the history book states 
that Rome was occupied by Caesar; (2) we still try to experi- 
ence, as well as we can, the wider meaning of this statement, 
i. e. y what a Roman citizen must have felt, how Caesar him- 
self must have felt, etc. In the first case, if our judgment is 
challenged — suppose it maintained, e. g., that we have mis- 
read the book, that there is no literary evidence for Caesar's 
having occupied Rome — in such a case, the only possible 
appeal is to direct sensory experience of the printed page. 
The doubter must read for himself, and have direct sensory 
experience of the printed symbols, in order to reconstruct for 
himself their meaning. The final appeal is certainly here to 
the sensory element in experience, and the thought appears to 
be a complex perceptual judgment. "The book has black 
marks in it" is obviously a judgment of perception. If the 
black marks are regarded as symbols, "The book contains 
symbols" is still a perceptual judgment. So too with the 
thought that the book contains letters, words, English words, 
the definite English words "Rome" "Was" "Occupied" "By" 
"Caesar." In short, the judgment "The book states that Rome 
was occupied by Caesar" is a complex perceptual judgment, a 
legitimate extension of the direct sensory apprehension of the 
letters in the book. Or if it is the associations that we empha- 
sise, by means of which we are able to read printed symbols, 

* What in a history book is less than the total judgment is equiva- 
leat to what, in a work of fiction, is the entire judgment — i. e., where 
no claim to represent the external course of actual events is made. 



30 VALIDITY AND THE SENSORY ELEMENT 

in that case we have a judgment of experience. In both cases, 
however, the appeal is certainly to direct sensory apprehen- 
sion, and that is the final sensory evidence for the validity of 
our judgment. 

The second part of our judgment is an extension of the 
meaning which we apprehend in reading the book. If asked 
with what right we build up some approximation to the expe- 
rience of Caesar and the Roman citizens, we can only state 
that it is a legitimate extension of the meaning of what we 
have before us. As we read the printed symbols, the sensory 
experience of the meaning of the words ''Rome," "Occupied 
by," "Caesar," etc., expands so as to include appropriate ele- 
ments from our own experience in one continuous whole, so 
that, so far as this personal experience permits, our reading 
is no neutral exercise in spelling, but is a fuller, richer, more 
adequate experience which approximates to the actual life 
about which we are reading. We cannot feel the actual glow 
of triumph which animated Caesar's veterans, or the confu- 
sion and blind panic of the partisans of Pompey. We do not 
know the Italian sky, the Roman crowds. But we have all had 
some experience of triumph, or panic; we fcave all experienced 
warm suns, blue skies, jostling crowds. And out of such expe- 
riences we can piece together something which comes to us 
with the warmth and intimacy of personal experience, and at 
the same time represents for us, by analogy, a pale copy of 
the experiences symbolised, the Roman scenes about which we 
are reading. The validity of this reconstruction rests wholly 
upon the meaning of the documentary evidence before us. 
We must abstract from misleading associations and uncritical 
interpretations, and confine ourselves to legitimate expansion 
— the extension authorised by what we read. In other words, 
the validity of the symbolic judgment rests on the same evi- 
dence as the experiential judgment; as far as it goes, it is to 
the sensory element that we must at last appeal, as the touch- 
stone of its validity. 

(D) In Transcendent Judgments.— Transcendent judgments 
represent, in extreme form, an element which has been grad- 
ually forcing itself upon our attention in the preceding cases. 
In the inductive generalisations of empirical science, i. e., in 
judgments of experience, the utmost we can do is to approxi- 
mate to certain knowledge. There is always some slight gap 
between the law we wish to establish, and the evidence on 



IN TRANSCENDENT JUDGMENTS 31 

which it rests. Inductive evidence can come as close to com- 
plete proof as we please; but there is always some falling 
short, some inability to establish perfect certainty. In the 
symbolic judgment, this gap is still more noticeable. Reor- 
ganise and reconstruct our personal experience as we may, 
we can never quite enter into the experiences of others, or 
into experiences which have never yet been ours. Analogy, 
similarity, even partial identity — but we always fall short of 
full identity, always fail to pass completely the gulf which 
separates desire from performance. In other words, our actual 
experience always falls short of the ideal which, all uncon- 
sciously, drives us onward, and is the hidden root of that 
dissatisfaction with the not-quite-perfect, which fastens upon 
all of us at times. In the transcendent judgment, this ideal 
is more insistent, and the gap between what we actually attain 
and the perfection, the consummation of infinite desire, is at 
its greatest. We can never know Things-in-themselves, never 
experience the First Cause, the underlying Substance, the 
Divine, perfect, infinite experience in which all the illusions 
and weaknesses of our finite, pitifully thwarted efforts are 
transcended and made perfect in harmony. If empirical and 
symbolic judgments cannot be completely verified, how much 
more is this the case with transcendent judgments! It is of 
their very essence to pass beyond the realm of experience, of 
the definitely verifiable. They are not given in sense-experi- 
ence, but are constructed by idealising intelligence. "Things- 
in-themselves" mean things beyond that aspect which alone 
we experience; "God" is infinitely greater than the ideas we 
can form of Him; the "Vision Splendid" which guides our 
efforts towards a better, finer life, is broader, deeper, sublimer 
than anything we have known. How then can we, in the pres- 
ent case, ask whether the validity of such judgments depends 
on the sensory element in our thought? 

The case is, perhaps, not as hopeless as it appears. Tran- 
scendent judgments, as we have already seen, contain some 
sensory elements. The metaphysical concept of God does not 
stand out of all relation to human life: the sphere of ideal 
Divinity, though larger than mere humanity, includes all our 
experiences as a portion of itself; the finite is not only tran- 
scended by, but is contained in, the infinite. All ideals, in 
short, which can have tangible meaning for us, stand in some 
connection with our sensory experiences. Let us consider a 



32 



VALIDITY AND THE SENSORY ELEMENT 



concrete case, for instance, the ideal of personality. We form 
our concept by putting together appropriate experiences of 
our own, and then transcending them in the direction of a 
more inclusive, or rather an aZMnclusive concept. We can 
take, for example, the personality of the grammar-school grad- 
uate, of the high-school graduate, of the university graduate, 
and link them up with our present focal consciousness in a 
curve representing the development in personality, somewhat 
thus: — 




So far, we have a judgment of experience, a complex sum- 
ming up of many perceptions. But we can go a little fur- 
ther; we can produce the line of the curve a little beyond the 
point we have actually reached; we can look ahead, and, so 
far as we remain within reasonable limits, we transcend 



IN TRAXSCEXDEXT JUDGMENTS 33 

indeed actual experience, but remain within the sphere of 
possible experience. That is to say, we form a symbolic judg- 
ment, and the concept of a not-yet-experienced personality 
which we thus form is justified precisely so far as it rests 
upon, and is a strictly continuous expansion of, the sensory 
elements linked together in the experiential judgment. It is 
in fact an extended judgment of experience, and its validity 
depends on the accuracy with which we have avoided misin- 
terpretation and have remained faithful to the direct percep- 
tions of that experience. What then is the transcendent judg- 
ment? It is an extended symbolic judgment, a judgment which 
extends beyond the limits of possible human experience — a 
judgment which includes, indeed, all that we have experienced, 
but expands to infinity, to a77-inclusiveness. All our thoughts, 
feelings, and wishes, in a word all our experiences, so far as 
they contain inklings of an ideal — point beyond themselves to 
this infinite, in which every thought finds its ideal comple- 
tion, every feeling its full expansion, and every wish its per- 
fect satisfaction. Our whole life is lived in the midst 'of this 
infinite ocean, and there is no sensation, no element in our 
living experience, which does not naturally extend itself with- 
out limit, seeking to transcend its own finiteness and to 
attain the full completeness of absolute Reality. 

That such metaphysical constructions go beyond the imme- 
diate sensory elements of experience, we have already seen. 
And yet, if we wish to justify the validity of some such exten- 
sion, to what can we appeal, if not to the experience which is 
thus to receive its ideal completion and satisfaction? The 
concept of God must satisfy our ideal aspirations, the hopes 
embodied in our concrete, living experience. The ideal of 
Personality is surely a concept in which we find — developed, 
transformed, our baser parts transmuted — our own selves, the 
"true" self, at present hidden, thwarted, dwarfed by extrinsic 
circumstances, but to the eye of thought revealed in that full 
perfection which alone could completely satisfy us. In other 
words, like the symbolic judgment of which it is an extension, 
the transcendent judgment is dependent, for its validity, so 
far as we can here speak of validity, on the accurate and 
direct apprehension of the sensory elements which extend con- 
tinuously from the focal sensory consciousness. 

Conclusion. — Let us try to put together the results reached 
in considering the different types of judgment. In the pre- 



34 VALIDITY AND THE SENSORY ELEMENT 

vious chapter we saw that, in passing from the simpler to 
the more complex types of judgment, the intellectual element 
plays a greater part, while the sensory element plays at any 
rate a less direct part. We saw further that the direct sen- 
sory stimulus plays a greater part in the simpler judgments, 
while in the symbolic and transcendent types the stimulus is 
relatively overshadowed by elements from the sensory back- 
ground. In the present chapter we have deliberately neg- 
lected, so far as possible, the intellectual element. We have 
noted in passing that to judge, on the basis of a warmth-sen- 
sation, that ik The room is warm" requires intellectual elements, 
and that in experiential, symbolic, and transcendent judg- 
ments the gulf between direct sensation and full judgment has 
grown increasingly wider, i. e., that the intellectual element 
has played an increasingly greater part. But leaving to sub- 
sequent chapters all consideration of the part played by intel- 
ligence, we have confined ourselves to studying the impor- 
tance, for the validity of the judgment, of the directly appre- 
hended sensory elements. 

In estimating the validity of a perceptual judgment, which 
asserts the warmth, heaviness, redness, etc., of an object— i. e., 
which deals in sense-qualities — it is impossible to test its accu- 
racy without appealing to sense-perception, in which alone 
such qualities can be directly and satisfactorily experienced. 
Similarly in judgments of a more complex type, so far as 
these are based upon sensory experiences, any test of validity 
must, in the end, appeal to direct sense-experience; for com- 
plete satisfaction of the desire for validity we must be able 
to apprehend in one continuous connection the sensory expan- 
sion from the stimulus which includes the relevant elements 
drawn from the general sensory background of experience. 
The same is true of symbolic and transcendent judgments; so 
far as these contain sensory elements, we can pass upon their 
validity only so far as we come to apprehend clearly and with- 
out bias their continuous connection with the focus of sensory 
consciousness. So far as symbolic and transcendent judgments 
really follow without deviation the directions approved by the 
judgments of experience — i. e., so far as these extensions of 
the focal consciousness are governed strictly by elements ver- 
ifiable in sense-experience, so far they are valid. So far as, 
without violating this condition, they transcend sensory veri- 



CONCLUSION 35 

fiability, they may or may not, perhaps, be valid, but such a 
point cannot be decided by an appeal to sensory experience. 

To sum up: — So far as judgment contains sensory elements, 
our thought depends on sensory apprehension, and so far as 
the sensory apprehension to which we appeal is valid, so far 
the judgment, at least on its sensory side, is valid. In its 
simplest and most direct forms, sensory apprehension is ulti- 
mate and its validity beyond reasonable question. Conse- 
quently, so far as the sensory element in judgment can be 
reduced to these simplest and most direct forms of sensory 
apprehension, or to some legitimate and continuous extension 
of these,3 so far the judgment itself, on its sensory side, is 
valid. In other words, so far as judgment contains sensory 
elements, its validity depends wholly upon direct apprehen- 
sion of those sensory elements. So far as it contains elements 
other than sensory, nothing has been as yet determined as 
to its validity, though a suspicion has been expressed that the 
validity of other elements also will be found, in the end, to be 
verifiable only by reference to sense-experience. The consid- 
eration, however, of such non-sensory elements must be 
deferred to the succeeding chapters. 

3 Cf. Bosanquet, Logw or the Morphology of Knowledge. Vol. I, p. 
77 : "Reality is given for me in present sensuous perception . 
The real world, as a definite organised system, is for me an extension 
of this present sensation and self feeling . . . and it is the essence 
of judgment to effect and sustain such an extension. . . . The 
given and its extension . . . are continuous with each other 
. It is the character and quality of being directly in contact 
with sense-perception . . . that forms the constantly shifting 
center of the individual's real world, and spreads from that center 
over every extension wnich the system of reality receives from judg 
ment." 

FOR FURTHER READING 

H. Lotze, Logic, sect. 267, pp. 337-339. Chr. Slgwart, Logic, Vol. I, 
pp. 262-264. W. Wundt. Logik, (3rd Edit.), Vol. I, pp. 78-83. 

EXERCISES 

1. Is it necessary to appeal to sense-experience in order to justify 
the following : The sky is blue. This water is hot. This book is 
heavier than that? 

2. Is it necessary to appeal to sense-experience in order to justify 
the following : Fire burns. Water quenches thirst. Peaches are in 
season in September? 

3. Is it necessary to appeal to sensory experience in order to 
justify the following : This student has been below grade so often 
that it is mathematically impossible for him to reach a passing grade 



36 VALIDITY AND THE SENSORY ELEMENT 

this term. Nothing venture, nothing win. It's sure to be cold in 
January ? 

4. Is it necessary to appeal to sense-experience in order to justify 
the following : It is impossible for a thing both to be and not to be. 
Ex nihilo, nihil fit. The soul is a simple, uncompounded substance? 

5. Do novelists find it necessary to appeal to sensory experience, 
even when they describe such entities as we have never experienced, 
and probably never could experience? Take as an instance, any one 
of H. G. Wells' romances, such The Angel, The Sea-Lady, The First 
Men in the Moon, The War of the Worlds, The Invisible Man, The 
Food of the Gods. 



CHAPTER IV 
THE INTELLECTUAL ELEMENT IN JUDGMENT. 

The Intellectual Element. — What we understand by "validity 
of judgment" has not been exhausted in our preceding discus- 
sion. We have seen that a judgment is valid, so far as it 
really _forms part of the continuous stream of sensory experi- 
ence. But by "validity" we certainly mean more than "form- 
ing part of a continuous sensory stream." The very notion 
of validity, correctness, accuracy, truth, or however we name 
it, seems to go beyond this idea that it is "given" to us. We 
contrast a judgment which is valid, not with one which is non- 
sensory or discontinuous, but with a judgment which is 
invalid, unsound, false. For the great majority of logicians, 
judgment is concerned not so much with the sensory side of 
experience, as with intellectual truth and falsity. For sen- 
sory continuity they would substitute intellectual consistency, 
and would throughout appeal, not to sensory, but to intel- 
lectual standards of validity. From continuity as such, for 
example, we should never obtain fixity, definiteness, clear-cut 
outlines. Where everything is fluid, as in a process charac- 
terised by unbroken continuity, — in such a case sameness, 
identity, sharp distinction, i. e., the necessary instruments for 
the erection of complex thought-structures, are absent. Most 
logicians, accordingly, emphasise the intellectual side of judg- 
ment, and regard sensation as furnishing the material for 
thought, while intellect introduces its standards into this 
otherwise formless material, gives it definite form and out- 
line, identity and distinctness, and on the basis so provided 
elevates structures in which intellectual instruments have so 
far transformed the original material that a great thinker like 
Kant can assert that reason only apprehends what itself has 
constructed in accordance with its own laws. 

It is not quite correct to regard sensation as merely furnish- 
ing the bare material for thought. The sensory consciousness 
is no pure receptivity, no tabula rasa open to impressions from 
any and every kind of object alike. As we have seen, it is 

37 



38 INTELLECTUAL ELEMENT IN JUDGMENT 

already, in its simplest stages, shot through with instinct, and 
presents a rudimentary organisation. The animal conscious- 
ness, for instance, is not a chaos of unrelated sensory elements, 
but is an organised whole in which even abstract general ideas 
may play a part.i We cannot, therefore, regard all organisa- 
tion of the sensory elements as exclusively the work of intel- 
lect. And yet, what the central nervous system secures for 
the animal at one level of development, the intellect — perhaps 
here also by means of the nervous system — secures at a higher 
level. The function of intellect is undoubtedly a kind of organ- 
isation, but an organisation which, for full comprehension, 
must be regarded from the view-point, not so much of its sur- 
vival value for the organism, as of its conforming to its own 
peculiar standards, which are intellectual rather than bio- 
logical. 

In order to obtain a clear idea of the nature of this intel- 
lectual element in thought, we shall trace its function in 
judgments, starting with the more simple, and proceeding 
gradually to the more elaborate. 

(A) In Judgments of Perception. — In "This is red," "The 
room is warm," and similar judgments, the impulse which 
induces us to single out for special attention the redness or 
warmth of some object which stands out against the general 
sensory background, is probably not intellectual interest. It 
is usually some feeling which, at bottom, is instinctive. Such 
feelings lead us to distinguish between background and stim- 
ulus, and thus to organise in a rudimentary perceptual rela- 
tion "This" and "red," or "The room" and "warm." But at 
this level of consciousness the distinction is not clear-cut. 
The one is not yet a "background" and the other not yet a 
"special stimulus." Neither has as yet a precise identity in 
virtue of which they are distinguished sharply and clearly 
from one another and deliberately set over against each other 
in an intellectually self-conscious act of thought. The intro- 
duction of such standards as "identity," "difference," "dis- 
tinction within a wider whole which unifies," etc., in a word, 
the raising of the vaguely felt organisation of sensory con- 
sciousness to a higher power, is the work of intellect. Fur- 
thermore, if we have any reason to mistrust our judgment, as 



i Cf. Wundt, Logik, 3d edition, Vol. I, chapter 1, sects. 2-4. Cf. also 
Erdmann, Logik, 2d edition, chapters 11-14, pp. 65 and 71. 



IN PERCEPTUAL JUDGMENTS 39 

when the object is only dimly seen, or when our conclusion is 
denied by a second person, in such cases the critical self-con- 
sciousness with which we take especial notice and make a 
deliberate judgment, is intellectual, and involves reference to 
intellectual standards, which must be conformed to before we 
are satisfied. In such cases the judgment is accepted, not 
merely as conforming to sensory apprehension, but as fitting 
into a system, an organised whole, of judgments of the kind 
in question. In perceptual judgments this reference to a 
wider system of perceptual thought is not clearly present, 
unless our conclusion is challenged. But it is always a part of 
the intellectual background, and if asked to justify our judg- 
ment, there is always some direct reference made to this sys- 
tematic, self-consistent unity of our thought. 

Let us emphasise the difference still further. Sensory appre- 
hension of "This," "red," "warm," etc., is vague, not precise, 
without outlines, not clear-cut, and forms part of a living 
stream of consciousness which extends continuously from the 
focal present in many directions without limit. Intellectual 
apprehension of the same qualities is sharply defined, an 
apprehension of entities taken out of the stream, and delimited 
against each other in such a way that their natures, that 
which makes them what they are known to be and distin- 
guishable from what they are known not to be — stand out as 
clearly envisaged identities. Sensory apprehension is an 
awareness of qualities in the living kaleidescope of flowing 
consciousness. Intellectual apprehension is the result of an 
analysis which takes the constituent elements out of their 
movement in the kaleidescope and subjects them, one by one, 
to the scrutiny of our mental microscope, and studies them in 
their own individual natures, as well as in their sharply 
defined relations to other contrasted elements. For sensory 
apprehension, every moment of our changing life is new, a 
variegated texture of experience in which no element is ever 
apprehended a second time in quite the same setting. Just 
as we cannot step into the 4 same stream twice, because the 
water into which we stepped before is now washed away 
down-stream, so the red which we experience today is not 
the same as the red which we experienced yesterday. Exter- 
nal conditions have changed; we also have changed. Yarium 
et mutabile semper homo. For intellectual apprehension, on 
the contrary, all is fixed and definite. The redness of a sen- 



40 INTELLECTUAL ELEMENT IN JUDGMENT 

sory experience is abstracted from its sensory context, is cut 
off and fixed by the mind; and for the intellectual elaboration 
of perceptual experiences we use, not directly apprehended 
sensory elements, but a kind of mental counters, not a par- 
ticular red or warm, but universalised qualities, red-ness, 
warm-wess, qualities that never were on sea or land, artificial 
entities, abstractions, non-living, discontinuous, conceptual 
identities. The function of intellect in judgments of percep- 
tion is thus to introduce, into the continuity of sensory expe- 
rience, ideals of identity, difference, and organisation. The 
elements thus hewn out with our mental hatchet are so trans- 
formed that they constitute portions of an intellectual system, 
amenable to standards of consistency, systematic unity, and 
identity. 

(B) In Judgments of Experience. — In "The freight trains 
crossing the bridge grow more troublesome every year," and 
similar judgments, the sensory element consists, as we have 
seen, in so extending the focal consciousness of the low rum- 
ble as to include in one continuous experience, not only the 
spatially distant train of the present, but also the temporally 
distant trains of the past. The associations from past expe- 
rience, by the aid of which this is accomplished, are fused 
with the focal ly present rumble-sensation, and constitute an 
integral portion of the unbrokenly continuous sensory con- 
sciousness, the complex perceptual judgment which we call a 
judgment of experience. Certain elements in the judgment 
appeared to us to be definitely intellectual, especially the "com- 
parison" of the past trains with the present rumble. For the 
rest, the interpretation of the rumble as a present train, and 
the recall of past trains, together with associated feelings of 
annoyance at the disturbance so occasioned — all this might 
well take place on the sensory level of consciousness. In the 
usual run of things, such a judgment, expressing, as it does, 
mere general annoyance at being disturbed, would not tend to 
rise much above the sensory level. But where it is thought 
advisable to establish such judgments of experience more 
firmly, or where we are not content with a vague general 
impression but insist on investigating further the phenomenon 
in question — in such cases we raise the judgment to a higher 
power by introducing exact intellectual standards. 

How is this accomplished? We analyse or split up the con- 
tinuous experience into a number of special cases of trains-on- 



IN EXPERIENTIAL JUDGMENTS 41 

the-bridge, and pass these special cases in review, one by one, 
noticing in each case, as well as we can, the comparative 
amount of disturbance thus caused. The distinction of these 
special cases from one another, and the careful attention to 
the disturbance occasioned by each one, considered by itself, 
gives us a far clearer basis for our comparative judgment as 
to the increase of the disturbance in question. The intellectual 
standards thus introduced are (1) identity — the introduction 
of which gives us units sufficiently equal or identical for com- 
parative purposes, viz., the individual train-disturbances; (2) 
difference — the introduction of which enables us to separate 
out and distinguish, both from one another and from expe- 
riences which are irrelevant, the various unit-experiences on 
which the judgment is based; and (3) organisation — the intro- 
duction of which enables us so to classify and arrange these 
disturbance-units within the wider system of our general expe- 
rience, that we can conclude as to the increasing annoyance, 
within that system taken as a whole, of the rumble due to 
the passing trains. In place of the continuity and vague flow 
of actual sensory experience, we thus have sharply differen- 
tiated, isolated train-disturbance experiences, compared with 
one another in the light of general principles of organisation. 
The clearness thus introduced is due to a definite transforma- 
tion of the original experiences, and the intellectual side of 
judgment is based always upon elements thus torn from their 
living context and fixed, universalised, organised on princi- 
ples, not of sensory continuity, but of strict relevance, con- 
sistency, conformity to intellectual standards of systematic 
unity and truth. It is in this way that bare sensory expe- 
rience is taken up into the structure of an empirical science 
based on judgments of experience. 

(C) In Symbolic Judgments. — In "Rome was occupied by 
Caesar" and similar judgments, the sensory side consists of 
elements taken from different strata of our conscious life and 
so re-arranged as to present, with something of the warmth 
and intimacy of personal experience, an analogy to the expe- 
riences actually lived through by Caesar and the citizens of 
Rome at the time of which we are reading. The nature of 
the part played by intellect is here conspicuously plain. In 
the taking elements from different experiential strata, i. e., in 
the tearing from their living contexts what we need for our 
purposes of construction, we clearly see the introduction of 



42 INTELLECTUAL ELEMENT IN JUDGMENT 

the standard of identity. With the idea of one identical expe- 
rience-type in mind, we pass in review the scenes from our 
past which association presents, and single out only what 
passes the test and conforms to our standard. By introduc- 
ing the standard of difference, we are able to distinguish and 
omit from the reconstruction everything in the experiential 
context which is irrelevant to the demands of identity. 
Finally the standard of organisation enables us so to reor- 
ganise these mutilated experiential fragments, as to recon- 
struct something consistent with the wider system of life 
which extends from the present to the time of Caesar, and is 
guided in detail by the text of our history book. 

In symbolic judgments there is, however, yet further evi- 
dence of intellectual transformation of the original experi- 
ences. The unit here is not merely the isolated triumph and 
panic-experiences, but is something still more artificial, still 
more conventional. So far as our judgment is an expansion 
on the basis of the printed symbols before us, the ultimate 
units are these symbols themselves. It is on the apprehension 
of these devitalised, conventionalised, universalised elements 
that our reconstruction of the meaning of what we read is 
ultimately based. Perhaps we can realise the part played by 
such conventional symbols more clearly in a different instance. 
Take the case of a problem about ducks, or workmen, or time- 
pieces, solved by simultaneous equations; take the case of the 
distance of a ship at sea, discovered by an appeal to trigono- 
metry; take any case of the movement of bodies, worked out 
in mathematical physics. In all such cases, the raising the 
problem from bare sense-experience to the intellectual level 
means the substitution of identical, conventionalised elements 
in place of the original continuity of life, and it is on the 
organisation of such symbols, strictly treated as such, that 
the certainty of the conclusion depends. In taking up our 
sensory experiences into the structure of empirical science, 
an enormous part is played by the introduction of such con- 
ventional identities, and it is hardly too much to say that our 
experiences admit of scientific manipulation only so far as 
they can be organised and formulated in terms of such sym- 
bols. 

(D) In Transcendent Judgments. — Transcendent judgments, 
as we have seen, constitute a kind of extended symbolic judg- 
ment. The elements, for instance, from which we construct 



IN TRANSCENDENT JUDGMENTS 43 

our concept of the ''infinite attributes of God," are taken from 
our own experience, and the resulting ideal represents man 
writ large — so large as to extend to infinity, i. e., infinite 
knowledge, infinite power, infinite justice, etc. In symbolic 
judgments the conventional identities separated out and organ- 
ised still retain some relation to our experience, and it is from 
their fringe of associations that they have meaning for us. 
That is to say, the conceptual identities on which the judg- 
ment is based are not entirely cut loose from experience; it is 
mutilated fragments which we put together, torn, if we will, 
from the living experiential context, but still retaining some 
semblance of life, some clinging strands which bind them to 
our personality and make them ours. In that extension of 
the symbolic judgment which we call transcendent, however, 
this relation is reversed. Our experience is here regarded as 
an isolated fragment torn from its true place in the Infinite 
Experience; to consider it as our own, as constituting a finite 
unity in itself is, for transcendent thinking, a fundamental 
error. We must learn, on the contrary, to view everything 
sub specie aeternitatis. It is the Divine Experience, of which 
we can construct the outlines, which is real and concrete; it 
is our sensory experience, with its continuity in space and 
time, which is fragmentary, riddled with contradictions, 
unreal, abstract. To arrive at metaphysical truth we must 
start, indeed, with our human experience; but by strictly 
introducing the standards of identity, difference, and organ- 
isation — far more strictly than in experiential and symbolic 
judgments — we pass, step by step, from the ideas of human 
goodness, human knowledge, and human power, to greater- 
than-human, and finally to ideas of absolute, infinite, Divine 
goodness, Divine knowledge, Divine power. It is by the strict 
introduction of these intellectual standards that we not merely 
reach the extreme limit of possible human development in 
goodness, etc., but ultimately cut ourselves loose from the 
remaining strands which bind us to humanity, and arrive at 
ideas which far transcend these in dignity and power. We 
use these intellectual standards as a kind of tower by which 
to climb the steep ascent of heaven. After the top of the 
tower is reached, in physical reality we could mount no higher: 
but knowledge is not a physical tower, and has no such limi- 
tations. From the purely human standpoint, it would seem 
as though the more strictly we introduce the standards of 



44 INTELLECTUAL ELEMENT IN JUDGMENT 

identity, difference, and organisation, the more attenuated 
becomes the living, sensory experience with which we start, 
and the more formal, artificial, and devitalised become the 
concepts which we thus construct, until finally the symbol is 
cut loose from life as we know it, and sense is lost in intel- 
lectual vision. For the metaphysician, on the contrary, this 
death to sense is the beginning of intellectual life, and in the 
ultimate constructions of transcendent thought we shake off 
the fetters which bind us to the earth below, and become one 
with the ideal which is also the only real, and by way of 
the intellectual love of God, enter directly into the Divine 
Experience. 

Conclusion. The Function of Intellect. — If we now put 
together the results of our enquiry in the present chapter, we 
realise that, as in other spheres of life, so also in the realm 
of thinking, the function of intellect is to organise our life- 
processes and make them significant and rational. The con- 
text of living sensory experience contains much which is irrel- 
evant and accidental, due to considerations of place and time. 
Our intellectual analysis leaves us with sharply differentiated 
identities, taken out of this context and stripped of all irrel- 
evancies — timeless and placeless entities, mental counters 
which can be put together in accordance with the demands of 
systematic unity. Out of these elements we proceed to build 
up an edifice of thought, a structure based on principles which 
are intellectual rather than sensory. It is like introducing 
the card-index system into our- business — in this case, the 
business of thinking. We can now take hold of our experi- 
ences, sort them out and handle them, shuffle and manipulate 
them in such a way as to gain all the advantages of scientific 
efficiency; and the resulting clarity and distinctness are 
undoubtedly a real gain. 

But there is another side to this process of intellectual 
analysis. Something has been lost which can not be replaced. 
The elements into which we have analysed our experience are 
no longer fluid and living. They are discontinuous, fixed, 
rigid, lifeless. They are like the separate pictures which a 
moving-picture artist puts together to represent some drama 
of real life. The utmost which the scientist can do in order 
to visualise intellectually the life which he has split up into 
fragments, is to put together the separate pieces in such a 
way as to simulate the original movement and continuity. But 



CONCLUSION 45 

the result is always jerky, unnatural, interrupted by flashes, 
by sudden transitions, by small flaws in the film. When all 
is done, it remains artificial, mechanical, a photographic imi- 
tation of life. The scientist is like a child with a toy which 
he has taken apart. He understands now how it works, but 
not all the king's horses and all the king's men can put 
together that unsightly heap of torn flesh and dissected organs 
which was once a living frog or embryo chicken. Thus we 
see that the introduction of intellectual standards of identity, 
difference, and organisation gives us clearness, certainty, 
science; but at the same time we realise that this clearness 
has been bought with a price: and it is a question how far 
the transformations wrought by intellect are legitimate. 
Before, however, entering upon this question — the general 
question of validity — we must study more in detail what is 
meant by identity, difference, and organisation. 

FOR FURTHER READING 

J. Dewey, Essays in Experimental Logic, pp. 220-229. H. Lotze. 
Logic, pp. 10-18. A. Riehl, Der phUosophische Kritieismus, Vol. II 
chapter i. W. Wumdt, Logik, (3rd Edit.), pp. 74-90. 

EXERCISES 

1. What precisely are the intellectual elements in the following: 
That suit looks old. These nasturtiums have an unpleasant odor. 
The corn grows larger here in the sun than what I see there in the 
shade ? 

2. What precisely are the intellectual elements in the following 
judgments : What we call "robins" are usually starlings. Mr. X's 
hand-writing is nearly always illegible. In the more northerly States, 
a closed sun-porch is of more use than an open screened-in porch? 

3. Wihat precisely are the intellectual elements in : There is no 
Royal Road to success. Income : $100.00 ; expenditure : $99.99 : 
result : happiness. Expenditure : $100.01 ; result : misery. According 
to results based upon statistics, I should expect three members of this 
class to receive the grade A? 

4. What precisely are the intellectual elements in the following : 
Whether it falls within the sphere of possible experience or not, the 
world must be rational, through and through. I solved the riddle of 
the universe. Virtue, though chained to earth, will still live free ! ? 



CHAPTER V 
IDENTITY. 

Identity or Sameness. — What do we mean by "identity"? 
We should usually say that any one thing or idea is identical 
with itself, is the self-same thing that it is: beauty is beauty, 
x = x, etc. Where we have what appear to be two entities, 
we should call them identical if they were the same in all 
respects; e. g., two triangles on the same base and with the 
same apex would coincide or fall together absolutely. They 
would be identical, and taken strictly we might maintain that 
there was only one triangle present. Identity thus excludes 
diversity or difference; so far as entities are different, they 
may be equal, but can never be strictly identical. E. g., 
X 2 — 2/2— (x+y) (x — y). Both sides of this equation lead 
to the same result: but the intellectual operations of squaring 
and subtracting, on the one side, are balanced by different oper- 
ations on the other, viz., addition within brackets, subtraction 
within brackets, and multiplication of complexes. The two 
sides of the equation are thus equal, but not absolutely the 
same, not identical. 

Let us apply this to logic. We have stated that intellect 
introduces identity as a kind of standard for organising our 
otherwise somewhat chaotic sensory experience. This means 
that intellect singles out from the heterogeneous mass of 
sensory elements those which are of one and the same kind, 
and regards these as units, as identical points with reference 
to which our thought builds up its characteristic chains of 
judgments and inferences, the elaborate structures of science 
and art. Let us consider in detail how this introduction of 
identical points of reference takes place. 

(A) In Judgments of Perception. — Take such a case as 
"This room is warm." We are seated in the room, and direct 
our thought to the temperature, neglecting the geometrical, 
social, and other features of the room. Omitting from con- 
sideration all other elements in the sensory environment, we 
single out only such stimuli as have one and the same refer- 

46 



IN PERCEPTUAL JUDGMENTS 47 

ence, i. e., stimuli which possess temperature value. In this 
way we come to judge that the room is warm. The warmth 
of the room is thus one unit within the judgment, an identical 
point of reference around which our thought, which was 
previously vague and fluid, crystalises and becomes clear and 
precise. Another such unit within the judgment is undoubt- 
edly "the room." This unit is constituted by direction of our 
thought to those features of our sensory environment which 
all alike are connected with the place where we are seated, 
rather than to the hundred and one other elements which 
might similarly have been selected as starting-points for judg- 
ment: e. g. y our work, our furniture, other people in the room. 

In this way, in place of the vague fluctuating mass of rela- 
tively unorganised sensations, we come to have a new organ- 
ised unity, our judgment, and within this judgment two spe- 
cial unities, the starting-point and the end-point of our 
thought. These two special units, "The room," with which 
we start, and the "Is warm," which represents our further 
determination of "The room," — are recognised by logicians 
under the names "logical subject" or 8, and "logical predicate" 
or P. 8 means the subject of discourse, what we are thinking 
about, and P means what we judge or think about 8. They 
are thought with reference to one another; the room is 
thought of as being warm, and warmth is thought of, not in 
a general way, by itself, but in definite relation to the room. 

The logical distinction between 8 and P should not be con- 
fused with the grammatical distinction between subject and 
predicate of a sentence. One and the same thought can have 
a hundred modes of grammatical or rhetorical expression, and 
it is easily possible for £ to be expressed by the predicate 
of a grammatical sentence, and for P to be expressed by the 
grammatical subject. Usually, indeed, there is a tendency for 
$ and the grammatical subject to coincide; but there is no 
necessary connection between the order of thought and the 
order of verbal expression. Consider, for example, "It is warm 
in the room," "Warmth is the most pronounced feature of the 
room," "Warm ist das Zimmer." These are three different 
ways of expressing one and the same thought, and if "The 
room" is the subject of discourse, it remains the subject of 
discourse whatever the grammatical or linguistic vehicle of 
expression. Or again, if I am discussing the subject of warmth, 
so that "warm" or "warmth" is 8, the subject of discourse, 



48 IDENTITY 

I might say, "Warm is . why, the room is warm, 

the fire is warm, the water from this faucet is warm, etc." 
In this case, "warm" still represents the logical subject, while 
"the room," "the fire," "the water from the faucet," etc., rep- 
resent new logical predicates, units singled out of the sensory 
environment in order to explain or determine further what 
we are thinking about, viz., "warm." Thus we see that S 
and P are independent of grammatical distinctions,! and in 
the case of perceptual judgments, we can conclude generally 
that our thought organises the vague flow of sensory con- 
sciousness by crystalising around two points of reference, a 
starting-point and an end-point of judgment, $ and P, respec- 
tively. This introduction of the standard of identity gives us 
clearness, definiteness, and precision, an intellectualised basis 
for the further organisation of our thought. 

(B) In Judgments of Experience. — In such a judgment 
as "The freight-trains crossing the bridge grow more trouble- 
some every year," we are seated at work, and are disturbed 
by the rumble of a passing train. Our reaction to this disturb- 
ance expresses itself in a feeling of annoyance, and with 
this feeling in mind, we omit from consideration all other 
elements in the environment, and single out from our experi- 
ences only such as have one and the same reference, viz., com- 
parative annoyance-value of this type. In this way we come to 
judge that the disturbances are growing more annoying every 
year. The increasing annoyance of such disturbances thus 
constitutes one unit within the judgment — an identical point 
of reference around which our experiences, which were pre- 
viously fluid, vague, and somewhat chaotic, become organ- 
ised, determinate, fixed. In place of the vague continuity 
of annoyed feeling, we have reached a definite conclusion, 
in which we can rest. Another such point of reference is 
undoubtedly the disturbance-due-to-freight-trains. This fur- 
nishes the starting-point of our judgment, and it is of this 
freight-train disturbance that we judge, that it "is growing 
more troublesome." As a unit of reference it is constituted 



1 We may further suspect that in reading or hearing a grammatical 
sentence taken out of its context, it is impossible to say with certainty 
what is the subject of discourse. From such a statement as "That 
is a tree/' taken by itself, it is impossible, apart from the context, 
to decide whether it is "trees" which are being spoken of, in which 
case "Tree" is S, and "That" is P, or whether "that object" is being 
discussed, in which case "That" is S, and "is a tree" is P. 



IN EXPERIENTIAL JUDGMENTS 49 

by concentration of our thought in the one direction, and by- 
omitting from consideration our work, the room we are in, 
and the hundred and one other features of the sensory envi- 
ronment in which we might have been especially interested. 

In this way, in place of the general attitude of attention 
to our work, with vaguely felt impressions coming in through 
all the avenues of sense in an unorganised manner, we come 
to have a new organised unity, our judgment concerning the 
increasing annoyance of train-disturbances. Within this 
judgment we have two subordinate unities, (1) the starting- 
point of our thought, viz., the disturbance, and (2) the end- 
point, viz., that it is growing more troublesome. The dis- 
turbance due to freight-trains is thus the subject of discourse, 
or S, and the thought that such disturbances "are growing 
more troublesome every year" is what we judge of 8, i. e., is 
the logical predicate, P. The introduction of the standard of 
identity thus gives us, in place of the irrelevant and chaotic 
elements which form part of our continuous experience merely 
because they have happened to us, for the most part as mere 
events without rhyme or reason — in place of this relatively 
unmeaning and unorganised continuity, the introduction of 
identity gives us clearness, relevance, definiteness, an intellect- 
ualised basis for the further organisation of our thought. 

(C) In Symbolic Judgments. — In such a judgment as 
"Rome was occupied by Caesar," we are reading a history 
book, and, in order to realise and make vivid to ourselves 
the meaning of what we read, we summon from our personal 
experiences all which have one and the same reference, all 
which in some way bring to our mind feelings of panic and 
triumph suitable to the occasion, the alarm of the Pompeians 
being balanced by the triumph of Caesar's friends. In this 
way we come to realise, as well as we can, what "occupation" 
means, and thus to think fully, or to judge, with full under- 
standing of the meaning of our judgment, that Rome "was 
occupied by Caesar." Was-occupied-by-Caesar thus furnishes 
one unit, one point of reference within the judgment, around 
which the rough mass of associated experiences becomes gradu- 
ally organised, and crystalises in definite clear-cut form. An- 
other such nucleus of organisation is furnished by "Rome," 
the general scene and background against which the various 
episodes of Roman history successively stand out. It is the 
starting-point of our judgment, and is constituted by the ox- 



SO IDENTITY 

ganisation of all of our experiences which relate in any way to 
the Eternal City. It arises in our minds as a unit of reference 
when we direct our thought only to such elements of our experi- 
ence as are connected with the great city about which we are 
reading, to the exclusion of other subjects of possible interest. 
"Rome" is thus the subject of discourse, the S of our judg- 
ment; "was occupied by Caesar" is what we judge about 
Rome, i. e., is the logical predicate, P.2 

In making this judgment, what have we effected? In place 
of the general attitude of mind consequent upon reading, with 
vaguely continuous sensory impressions coming in through 
eye, ear, etc., and vaguely aroused associations from past 
experiences, unorganised and irrelevant but all forming part 
of the cross-section of our conscious life, we have now a 
sharply distinguished, clear-cut unity, the judgment that 
"Rome was occupied by Caesar." Within this unity we have 
two definite unities, (1) Rome, the background of our history 
and starting-point of our judgment, and (2) "was occupied 
by Caesar," the new determination of our thought of "Rome," 
the end-point or logical predicate of our judgment. These two 
units, Rome and was-occupied-by-Caesar, are clear fixation- 
points introduced as identical points of reference by the intel- 
lect, and furnish an intellectualised basis for the further 
organisation of our thoughts, as we build up for ourselves 
an adequate conception of History. 

(D) In Transcendent Judgments. — If we compare the logical 
subjects in the various types of judgment considered hith- 
erto, "The room," "Freight-train-disturbances," "Rome," we 
notice at once that, while all alike are units or identical 
points of reference within their respective judgments, yet 
the later ones are increasingly complex. "The room" is a 
matter chiefly of present sensory experience; "Freight-trains", 
include not only present sensory experience, but also the 
relevant experiences which go back for some years; and 
"Rome" furnishes a centralising nucleus for very many and 
very complex experiences. So too when we compare the 
logical predicates. "Warm" is a relatively simple experience 
as compared with "grow more troublesome every year," and 

2 It is assumed in the text that it is a "History of Rome" which 
we are reading. If, however, the sentence occurred in a "Life of 
Caesar," so that Caesar and his actions constituted the main subject 
of discourse, then "Caesar" would be 8, and "Rome-occupied-by-him" 
would be the further determination of this subject, which we call P. 



IN TRANSCENDENT JUDGMENTS 51 

this again is less complex than the innumerable series of 
experiences which are organised with reference to the idea 
of "was occupied by Caesar." As we have seen before, judg- 
ments of perception are organisations chiefly of immediate 
sensory experiences; judgments of experience include also 
associations from past actual experience of the subject of 
discourse; while symbolic judgments go beyond this, and 
include all possible experience, i. e., all combinations of actual 
experiences which the mind can construct suitably to the 
occasion. This is more complex than what we find in the 
experiential judgment, for there we are confined to those 
experiences which have actually occurred in the combination 
in question, whereas in the symbolic judgment we rearrange 
and re-combine elements originally experienced in other com- 
binations, and thus have a much larger stock of experiences 
on which to draw. If, then, the same rule is exemplified in 
transcendent judgments also, we shall expect to find that the 
identical points of reference introduced into this class of judg- 
ments are the most complex and far-reaching of all. 

Consider such a case as "God is a substance consisting in 
infinite attributes." The logical subject here is, presumably, 
"God," and the logical predicate "is a substance consisting in 
infinite attributes." The term "God" includes all our experi- 
ence, both actual and possible, and is thus the most complex, 
all-inclusive idea that we can form. And if we go still further, 
and include in the idea not only all possible human experi- 
ence, but also the thought of experiences infinitely wider and 
deeper than anything which any human being can know, we 
include not only all possible human knowledge, but go beyond 
this, and launch out upon the infinite ocean of the barely 
thinkable and imaginable. So too with the logical predicate 
of this subject. Not only spatial and mental qualities are 
ascribed to this substance, but they are attributed to it in 
an infinite degree, including all we could ever know, and 
more. And further, an infinity of other attributes, each one 
of which lies in the great Beyond, beyond anything of which 
we finite human creatures can even frame a concept, are also 
assigned to this substance. Thus we see that in the trans- 
cendent judgment, both $ and P reach the limit of inclusive- 
ness, the extreme limit of complexity. 

It remains to ask whether it is by using the principle of 
identity that we form these transcendent concepts. So far 



52 IDENTITY 

as a symbolic judgment is concerned, so far, that is, as out 
of the shreds and patches of our experience we construct an 
ideal man, a man writ large, if we will, but still humanly 
possible, still man — so far, we have already seen, it is by 
selecting from our experience only such elements as have one 
and the same reference, i. e., by introducing the standard of 
identity, that we construct the symbolic concept in question. 
But when we go further, when we transcend the humanly 
possible and construct the idea of something beyond what 
we could experience, something infinitely, Divinely perfect, 
not man-writ-large, but GOD — do we reach this transcendent 
ideal also by holding fast to some identical point of reference, 
or do we adopt some other method? 

The answer is that here also, beyond experience as within 
it, both 8 and P are formed by the aid of this identity- 
standard. The point of reference remains one and the same 
throughout. It is the idea of the "absolutely perfect." So 
long as we confine ourselves to human experience, we can 
only attain to rough approximations to this standard, and 
the resulting concept falls short of our ideal, remaining all 
too human, and limited by human imperfections. When we 
cut ourselves loose from the limitations of experience, we do 
not in any way change the main direction of our thought: 
we still proceed to build up the ideal of the absolutely per- 
fect. All that is new is that we select strictly and exclusively 
what conforms to this standard. We leave out of the picture 
those aspects of human nature which are finite and imperfect, 
and retain only the formal abstract essence of goodness, truth, 
power, etc., and even add the purely formal idea of other 
attributes not exemplified in our human experience at all. 
Thus we see that in the realm of complex feelings which 
spread out over the whole of our experience, the introduction 
of the standard of identity enables us to organise our experi- 
ences in a way which gives us at least clearness and pre- 
cision, and furnishes a definite basis for the further organi- 
sation of our thought. 

Conclusion: The Standard of Identity. — In all types of 
judgment, then, one function of intellect consists in selecting 
from our experiences all such as have one and the same 
identical reference, all which are strictly relevant to some 
definite subject of discourse, whether the field is sensory, 
experiential, or some symbolic or transcendent extension of 



CONCLUSION 53 

the field of direct experience. By introducing this standard 
of identity-of-reference we come to have, in place of the vague 
general flow of sensory consciousness (1) a sharply demarcated 
unity, which constitutes the judgment as a whole, e. g., "It is 
warm here," "This disturbance is excessive, ,, and (2) within 
this new field two subordinate unities, (a) a clearly envis- 
aged subject of discourse, or logical subject, and (b) a definite 
determination of that subject, viz., the logical predicate, "is 
warm," "is excessive." In this way, then, in place of an 
experience determined by the order in which things have 
happened to us — a chance medley of sensations, wishes, and 
feelings — we introduce an order determined by unity of mean- 
ing, relevance, and identical reference. 

FOR FURTHER READING 

B. Bosanquet, Logic, Vol. II, pp. 206-208. F. H. Bradley, Principles 
of Logic, pp. 131-135. B. Erdmann, Logik, (2nd Edit.), pp. 237-253. 
Chr. Sigwart, Logic, Vol. II, pp. 24-30, 80-92. W. Wundt, Logik, (3rd 
Edit.), Vol. I, pp. 552-553. 

EXERCISES 

1. How far does the standard of identity enter into the following : 
This mirror is dusty. I like this picture. That hurts? 

2. How far does the standard of identity enter into the following : 
Children are a joy, so far as my experience goes. The card-index 
system has increased the efficiency of my business. The cost of living 
has steadily gone up for the last three years? 

3. How far does the standard of identity enter into the following : 
Sea-sickness depends upon the functioning of the semi-circular canals. 
Bleriot was the first man to cross the English Channel in an air-plane. 
Little Bo-Peep has lost her sheep? 

4. How far does the standard of identity enter into the following : 
Things in themselves are the underlying ground of sense-perception. 
Oh, for a mansion in the skies ! A form of unutterable beauty 
appeared to me? 



CHAPTER VI 

DIFFERENCE. 

Introduction of Difference. — What do we mean by differ- 
ence? "A is different from £" means that A is distinguish- 
able from, other than, B; A and B are diverse; A and B can 
be separated^ from one another, can be set over against and 
opposed to one another, can be contrasted with and denied 
of one another. A is not B. A and B are not the same, do 
not constitute an absolute unity, an identity; on the contrary, 
they constitute a duality, a plurality. They are not one, 
but at least two, and can be sharply delimited against one 
another. Stated negatively, each is not what the other is; 
stated positively, each is what the other is not. Stated nega- 
tively, an electric bulb is different from a typewriter, because 
each fails to possess qualities essential to the functioning of 
the other. The bulb has no keys, no ribbon, no place for 
inserting paper, and thus cannot be used for the same pur- 
pose as a typewriter. The typewriter, on the other hand, has 
no transparent surface, no wires, no connection with an 
electric battery, and thus cannot be used to illuminate a 
room. They are thus sharply distinguishable or different 
from one another Stated positively, in order to emphasise 
the positive element on which the differentiation depends, 
each has its own identity, its own nature, that which makes 
it what it is. The bulb has the transparent surface and plat- 
inum wire, the machine has the keys and ribbon. Each has 
the qualities which fit it for the performance of its own 
special function, and it is in virtue of specialisation or differ- 
entiation of function that each cannot perform the other's 
function, and is thus different from it. If we apply this to 
logic, we see that "introduction of the standard of difference" 
will mean splitting up the stream of consciousness into 



i Separated, i. e. 3 in thought, not necessarily in reality. The con- 
cave and convex aspects of one and the same curve, for instance, can- 
not be separated in actuality, but can be separated in thought, and 
regarded as "different." 

54 



IN PERCEPTUAL JUDGMENTS . 55 

identities which are sharply distinguished from and con- 
trasted with one another. Let us consider more in detail 
what this means. 

(A) In Judgments of Perception. — Let us consider such a 
judgment as "This room is warm." Before we introduce 
intellectual elements into our thought and frame a judgment, 
our consciousness flows evenly at the sensory level. We are 
seated quietly at work, and a cross-section of our conscious- 
ness reveals, beside the complex work-interest, only a vague 
general background of feelings, incipient impulses, and half- 
apprehended sensations, all equally without distinction con- 
tributing to swell the fluid undifferentiated mass, in which 
no difference, no clear-cut outlines, have as yet been intro- 
duced. 

What change occurs when we introduce difference? In 
place of a continuous, undifferentiated mass of sensations, 
feelings, and impulses, we have the distinct sensation of 
"warmth" standing out in sharp contrast over against our 
previous state. This sensation forces itself upon our attention 
by excluding other conscious elements, and the more clearly 
we become aware of it, the more sharply do we distinguish 
it from the general sensory background. It constitutes a 
nucleus for introducing still further distinctions. We split 
up the stream of consciousness into elements, among which 
"the room" is also prominent. "The room" is "warm." Per- 
haps it ought not to be warm. The furnace needs attention, 
or there is a fire. In our judgment we thus have two elem- 
ents, "the room" and "warm," analysed out from the general 
conscious flow, separated, cut off and fixed by the mind in sharp 
distinction from one another. These two elements are what 
we have come to know as 8 and P. In the previous chapter 
we considered them as "identities" constituted by the posi- 
tive concentration of thought in some one direction. In the 
present chapter, we are considering them from a more nega- 
tive aspect, as differentiated or distinguished from one 
another: 8 is not P, and P is different from 8. 

Let us consider what this means. Suppose, if possible, 
that 8 and P were not distinct from one another. Take, e. g., 
such a statement as "The room is the room," "warm is warm." 
Such "identical propositions" — as they are called — are almost 
without meaning. As we approximate more and more to 
complete absence of difference, so do we approximate to com- 



56 DIFFERENCE 

plete absence of thought, of judgment. If the end-point is 
in no respect different from the starting-point, then we have 
never really started: there has been no movement of thought, 
no mental operation. It is, in fact, only where 8 and P are 
sharply differentiated, that a genuine judgment, in which 
something is actually thought, some problem solved, some 
conclusion reached — takes place. When Pilate says "What I 
have written, I have written," he means "What I have written 
stands, is unalterable, must and shall remain what I have 
made it": and it is precisely this difference between 8 and P 
which gives us the movement, the living element essential 
to meaningful thought. Thus we see that introduction of the 
standard of difference into our thinking is vital to judgment, 
and results in giving us the logical 8 and P, no longer as 
mere identities, but as sharply differentiated identities, clear- 
cut elements whose distinctness is essential to the intellectual 
organisation of our experience. 

These differences hold within the judgment itself. But we 
should also note that the judgment as a whole has been carved 
out of our sensory experience. The mental hatchet of differ- 
ence has thus separated off not merely the 8 and P of logical 
thought, but also the judgment as a whole, as an intellectu- 
alised complex, sharply distinguished from the previous state 
of mind. 

(B) In Judgments of Experience. — Consider such a case as 
"The freight-trains crossing the bridge are growing more 
troublesome every year." We are seated at work, when the 
distant rumble forces itself upon our attention. At once, in 
the place of the steady, even flow of consciousness in the 
direction of our work-interest, we have opposition, contrast, 
interruption. The in-breaking sensation interferes with and 
thwarts, for the moment, our work-interest, and is, so far, 
annoying. If our consciousness remains at the sensory level, 
we experience only a vague general sound-annoyance, which 
comes and goes. But if the stimulus persists, or is very loud, 
the experience tends to rise to the level of an intellectual ised 
thought, a judgment in which difference is clearly present. 
As we attend more and more to the rumble, the two elements, 
(1) of what the annoying rumble means, viz., freight-train- 
disturbances, and (2) the increasing troublesomeness of such 
disturbances, become clearly separated out and differentiated 
in our minds. The train-disturbances are becoming too 



IN EXPERIENTIAL JUDGMENTS 57 

troublesome; they ought not to be allowed to grow worse; 
some protest must be made. The steady, even flow of con- 
sciousness has disappeared, and in its place we have sharply 
opposed and clearly outlined elements, (1) train-disturbances 
in the past and present, and (2) the thought that these are 
growing increasingly troublesome. 

We thus have a judgment in which the two elements which 
we have come to know as 8 and P stand out prominently. In 
the preceding chapter, these were considered positively, as 
identities introduced by the concentration of our thought in 
definite directions. At present, they are being considered more 
negatively, as different from, distinguished from, and opposed 
to, or contrasted with, one another. They are contrasted identi- 
ties. Each has its own nature, but these natures are different, 
and it is the meaning of this difference for judgment, which 
we are trying to realise. Suppose there were no such difference. 
Suppose 8 and P coincided, as in "The freight-trains crossing 
the bridge are the freight-trains crossing the bridge." Is there 
any valuable element of meaning about such a statement? 
Would any one seriously regard such a form of words as 
expressing a judgment, an act of thought which might, e. g., 
cause the thinker to be treated as intelligent rather than 
imbecile? If there were really no shade of differences intro- 
duced between & and P, if they strictly coincided, clearly there 
would be no act, no movement of thought, no discovery, no 
new step, no solution of a problem, no intelligent behavior at 
all. In other words, in order to form a judgment, to think 
something which is meaningful, significant, to advance instead 
of to mark time, it is necessary to introduce the standard 
of difference into our thought. Only by so doing do we 
attain to that sharp differentiation of elements, that clear 
distinction of & and P from one another, which is essential 
to the intellectual organisation of our experiences. In place 
of the even flow of sensory consciousness, the buzz and hum 
of unreflective life, we now have, taken out of the stream of 
consciousness, carved out and separated off from one another, 
elements which have lost the continuity of their sensory 
character, and have become loosed from their context and 
intellectualised, fixed by the mind negatively as well as posi- 
tively — the differentiated identities, 8 and P. It is on the 
distinction, as well as the identity, that we depend for the 



58 DIFFERENCE 

new combination of these elements which gives us intellectu- 
ally organised experience, in a word, empirical science. 

Here also, as in the perceptual judgment, we may further 
note that, as within the judgment 8 and P are distinguished 
from one another, so also the standard of difference distin- 
guishes the judgments as a whole, as an intellectualised com- 
plex, from the sensory consciousness out of which it has been 
cut out and put together by the mind. 

(C) In Symbolic Judgments. — Let us consider such a judg- 
ment as "Rome was occupied by Caesar.'' To form a clear 
idea of the sensory level of the reading-consciousness, as dis- 
tinct from the intellectual level of clear-cut judgment, we 
must call to mind those states of fatigue or distraction, in 
which our eye has followed the symbols on the printed page, 
but our mind — as we eventually discover — has not taken in 
the meaning at all. It is possible for the eye to have made 
every adjustment necessary for distinct vision, it is possible 
for the hands to have turned over page after page in due 
course, and yet, when we look back on what we are supposed 
to have read, we discover, only too clearly, that our experi- 
ence has remained at the sensory level, and that we have 
no grasp on the subject-matter, no intellectual organisation 
of our visual sensations sufficient to give us an understand- 
ing of this chapter in Roman History. 

What happens, then, when we do rise to the intellectual 
level, and not merely attend to the printed symbols, but read 
into them the full meaning which they will bear? As we 
attend, e. g., to the word "Rome," the steady even flow of 
consciousness is arrested. We look before and after. We 
pause and think. The word we read serves as a nucleus for 
associations from our past experience. As we continue to 
attend, and think of Rome as "occupied by Caesar," we split 
up still further the massive stream of consciousness, sensory 
and associative. We analyse it out into minute elements, 
and select from our variegated experiences only such elements 
of panic and triumph as are suitable to the occasion. We 
exclude all which are irrelevant, different from what we are 
seeking. The concepts of "Rome" and "occupied by Caesar" 
which we thus construct are organised complexes, into which 
difference, as well as identity, has entered. The elements out 
of which they have been put together have been carefully 
selected, in such a way as to exclude all which are irrelevant, 



IN SYMBOLIC JUDGMENTS 59 

inappropriate, other than what is required. The "Rome" of 
our judgment is different from the Rome of Romulus, the 
Rome of Scipio Africanus, the Rome of Sulla. It is the Rome 
of Pompey and Caesar, faction-torn and fearful of proscrip- 
tions, in short, Rome as "occupied by Caesar." 2 So too the 
predicate-concept "occupied by Caesar" is not constructed out 
of panic-and-triumph elements in general, but of such elem- 
ents torn from their context in my own experience, and so 
split up, altered, re-organised, that they now represent, not 
my actual experience, but — something different, an experi- 
ence such as I might have had, had I been a citizen of Rome 
at the time of its occupation by Caesar. The sensory con- 
sciousness has thus become intellectualised by the introduc- 
tion of difference, as well as identity. 

A second way in which difference enters into the judgment 
is seen if we consider the subject and predicate concepts. 
"Rome" and "occupied by Caesar" are contrasted, set over 
against and opposed to one another. Each has its own nature, 
its own identity. But they are diverse natures, opposed iden- 
tities, and it is out of the clash and conflict between them 
that the dramatic significance of the judgment arises. A 
mother-city ought not to be "occupied" by one of her own 
sons. It is an outrage, none the less tragic because it was, 
perhaps, inevitable. 8 and P are thus different, distinct. We 
can, perhaps best realise the importance of this distinction, 
if we compare with the above judgment such statements as 
"Rome is Rome," "Caesar is Caesar," "Occupation is occupa- 
tion." Such "identical propositions" show colorless and life- 
less in the comparison. If we look still closer, they are 
even meaningless. If S and P are wholly without difference, 
if they coincide absolutely so as to be one identity, and not 
two, then there is no distinction between end-point and start- 
ing-point of our thought: which is as much as to say, there 
has been no act or movement of thought at all. Nothing has 
been accomplished, no problem has been solved, no'" meaning 
read into our sensations. In other words, difference is essen- 
tial to the symbolic judgment, and its function is, to split up 
the stream of sensory consciousness into sharply differenti- 
ated elements, out of which clear-cut, cleanly outlined com- 
plexes, S and P, can be constructed and set over against each 

2Cf. Lotze, Logic, sec. 58 (E. T., p. 63b). 



60 DIFFERENCE 

other in such a way as to produce meaning, significance, 
intellectual life. 

Finally, as in the preceding types of judgment, so here, 
we may note that difference enters not only into the elements 
out of which 8 or P is constructed, not only into 8 and P as 
wholes contrasted with one another in the judgment, but 
into the judgment as a whole. As an intellectualised com- 
plex, this judgment can not be too sharply differentiated from 
the even-flowing sensory consciousness out of which it has 
been constructed. 

(D) In Transcendent Judgments. — Take such a judgment 
as "God is a substance with infinite attributes". Transcen- 
dent judgments of this type are so far removed from the 
sensory level of consciousness, that it is difficult to determine 
with certainty the sensory background, and especially the 
particular sensory stimulus which induces us to dare the 
great venture, and seek a firm foothold for our faith beyond 
the possibilities of human experience. But, since any stimulus 
whatever may lead to pursue a train of reasoning beyond the 
bounds of experience, we may suppose something of the fol- 
lowing kind. We are in a "brown study," with a tendency 
in the direction of religious feeling. The most prominent 
factor in consciousness is simply vague feeling, at the undif- 
ferentiated sensory level. This feeling extends vaguely, i. e., 
without precise limits, over the whole background of experi- 
ence, and thus, as being without clear-cut limits, presents a 
kind of sensory analogon to infinity. If now the thought of 
some personal failure, for example, or the loss of a loved 
friend, leads us to think of our own helplessness, the aspira- 
tion after something better, finer, greater, less limited than 
ourselves arises as a correlative idea, and as we follow up 
this line of thought, we can hardly fail to pass beyond the 
bounds of space and time, beyond the border-line which 
separates the humanly possible from what we can never 
experience — to the idea of an absolutely perfect, ideal, Divine 
Being, in Whom we live and move, and from Whose view- 
point all our finite, human problems find their completely 
satisfying solution. This is the thought of God, and we have 
reached it by introducing a distinction between our own 
imperfect selves and a perfect, ideal self. It is thus a complex 
construction into whose organisation difference, as well as 
identity, has largely entered. Though at this level of thought 



IN TRANSCENDENT JUDGMENTS 61 

sensory feeling, perhaps, still plays a great part, it is feeling 
organised around the thoughts of (1) human self, (2) Divine 
Self, and (3) the vast difference, or rather impassable gulf, 
between them. 

From an intellectual feeling of this kind to the judgment 
that God (as experienced in this way) is a "substance with 
infinite attributes," is perhaps a far cry for one who may not 
have been educated in the technicalities of Aristotelian or 
Spinozistic terminology. We do not, perhaps, quite naturally 
interpret our feeling after an ideal Self in terms of "sub- 
stance" and "attributes." The terms are unfamiliar to us. 
But the thought behind this terminology, the idea which 
expresses itself in this kind of way, is familiar enough, and 
for our present purpose it is sufficient to note that such an 
idea as "substance with infinite attributes" is a complex idea 
into which difference largely enters. There is (1) the dis- 
tinction between substance and attribute, (2) the difference 
between the many distinct attributes united in this one infinite 
substance, and (3) the vast difference between these attrib- 
utes as we human beings know some of them, and these attrib- 
utes as extended to infinity, as they are ascribed to Divinity. 

Thus we see that, as in the symbolic judgment, so here, 
both subject-term and predicate-term are complexes into 
whose organisation difference, as well as identity, largely 
enters. The fact that in symbolic judgment we remain within 
the field of possible experience, whereas in transcendent judg- 
ment we pass beyond this to absolute infinity, does not seem 
to involve anything new in respect to the standard of differ- 
ence; for example, it does not involve our not introducing 
this standard. On the contrary, the intellectual element of 
difference seems to be introduced more sharply, in proportion 
as our thought travels further and further away from direct 
sensory experience. Within the field of experience, for 
instance, all differences are merely relative, and it is fre- 
quently possible for us to learn to pass over the intervening 
distances. But between Human and Divine, between finite 
and infinite, between relative and absolute, there is no ratio. 
Here the difference is such that we human beings can never 
learn to pass it. In fact, the whole point of the transcen- 
dent judgment is that it deals with extreme differences, with 
difference made absolute. 

It remains to notice another way in which difference enters 



62 DIFFERENCE 

into the transcendent judgment. Not only does difference 
enter into the organisation of elements which constitutes the 
complex & or the complex P, but 8 and P as wholes, as units, 
are different from one another. Both "God" and "substance 
with infinite attributes" may, it is true, be ways of naming 
that feeling after a perfect Self which we have briefly 
described above. But they are different ways of describing 
that experience, and we must try to realise the importance 
of this difference for the transcendent judgment. Consider, 
for instance, such a statement as "God is God," or "Substance 
is substance," or "Infinite attributes are infinite attributes." 
We see at once that, by comparison with "God is an infinite 
substance," such "identical propositions" (as they are called) 
are relatively colorless, and almost without meaning. In 
fact, if 8 and P are really intended in precisely the same 
sense, if there is no change or development of meaning, then 
no operation of thought has taken place, nothing has been 
judged. Difference between 8 and P is, then, vital to our 
transcendent thought, and serves to make possible that move 
ment and development in our thinking, in which something 
(P) is definitely judged of something else (8). 

Finally, yet another way in which difference enters into our 
transcendent thinking is seen when we compare, not 8 with 
P, but the judgment as a whole with the feeling-conscious- 
ness at the sensory level, from which our clearly articulated 
thought that "God is a substance with infinite attributes" has 
arisen. In place of the steady, even flow of this sensory con- 
sciousness we have elements torn out of their sensory contexts 
and placed together in a new order, in such a way as to con- 
tribute to that highly articulated organisation of intellect- 
ualised elements which aims not merely at summing up actual 
experience, or to express symbolically the meaning-values of 
an experience thought of as only possible — but which seeks to 
sum up and state the meaning of an experience which goes 
infinitely beyond what is possible for human beings, and 
transcends the range even of what we can clearly and con- 
sistently symbolise. 

Thus we see that the function of difference in the trans- 
cendent judgment is, to split up the sensory consciousness 
into intellectualised elements, on the basis of which a complex 
8 and a complex P, sharply distinguished from one another, 
are constructed, in such a way as to produce a single, highly 



FUNCTION OF DIFFERENCE 63 

organised judgment. This judgment, in its turn, is clear-cut, 
sharply outlined, and very different from the relatively unor- 
ganised mass of sensory feeling from which it originated. 
Each step of this construction is a function of difference no 
less than identity, and, so far as the transcendent differs from 
the symbolic judgment, so much the more strictly and rigidly 
has the standard of difference been introduced. 

Conclusion — The Function of Difference. — If we put together 
the results reached in considering each of the above types 
of judgment, we find that the introduction of difference into 
our thought splits up the even-flowing, continuous sensory 
stream into intellectualised entities. Out of these, by a proc- 
ess of selection and re-arrangement, the intellectually organ- 
ised complexes, 8 and P, are constructed, in such a way as 
to produce a significant judgment. Difference thus enters 
into judgment in three ways: (1) The elements out of 
which the complex 8 and the complex P are constructed, are 
sharply differentiated from one another; (2) 8 and P as wholes 
are clearly outlined and delimited against each other; (3) 
finally, the judgment as a whole is distinct from the sensory 
consciousness from which it has arisen. Without difference 
at each of these stages, there would be no distinctness in our 
thought, and if there were no distinctness in our thought, that 
intellectual organisation of sensory consciousness in which 
judgment consists, could not come into being. 

In the last chapter, we observed that the introduction of 
the standard of identity made itself noticeable in precisely 
these same three ways. What, then, is new in the present 
chapter? What is new is chiefly another kind of emphasis. The 
elements out of which 8 and P are constructed are identities; 
8 and P are themselves identities; and finally the judgment 
itself, whether sensory, experiential, symbolic, or transcen- 
dent, is an identity. This represents a positive aspect of that 
intellectual organisation which gives us judgment. In the 
present chapter, we have been emphasising a more negative 
aspect of the same mental operation. The identity which is 
8 and the identity which is P are distinct identities, held 
over against and contrasted with each other in one act of 
thought: and it is on this difference, as well as on identity, 
that the significance of judgment depends. Similarly, if the 
different elements out of which £ and P have been constructed 
were not sharply distinguished, we should have no clear-cut, 



64 DIFFERENCE 

distinctly apprehended, intellectualised complexes, but merely 
vague masses of sensory consciousness. Finally, if the identity 
which is the judgment as a whole were not very different 
from the relatively unorganised sensory consciousness, if it 
were not an articulated whole in which difference, as well 
as identity, played a large part, it would not be what we call 
a judgment. From this we conclude that identity and differ- 
ence are two correlative aspects of one and the same process. 
We can only differentiate entities which have natures of their 
own, such as the electric bulb and the typewriter; and sim- 
ilarly, if we are to apprehend clearly the identical nature of 
anything, we can do so only by at the same time distinguish- 
ing it from other identities which it is not. What, then, is 
this process, of which identity and difference are two correla- 
tive aspects? The answer to this question must be left to 
the following chapters. 

FOR FURTHER READING 

B. Bosanquet, Logic, Vol. II, pp. 208-210. F. H. Bradley, Principles 
of Logic, pp. 135-142. B. Erdmann, Logxk, (2nd Edit.), pp. 247-253. 
W. Wundt, Logik, (3rd Edit.), pp. 553-555. 

EXERCISES 

1. How far does the standard of difference enter into the follow- 
ing : Here we are. This typewriter is heavier /than that. I am 
thirsty ? 

2. How far does the standard of difference enter into the follow- 
ing : Nobody loves me — everybody hates me. There is usually an 
enormous difference between a freshman and a senior. Radishes tend 
to do well in spring? 

3. How does the standard of difference enter into the following : 
A straight line is the shortest distance between two points. Little 
Jack Horner sat in a corner. I can do tomorrow what I am leaving 
unfinished today? 

4. How does the standard of difference enter into the following : 
We ought to devote our lives to the service of the highest ideals. God 
loves us. Our love can never die? 



CHAPTER VII. 
ORGANISATION, (a) INTERNAL 

The Meaning of Organisation. — Perhaps we can best under- 
stand what is meant by organisation, if we compare an aggre- 
gate with a totality. A chance heap of stones is an aggregate, 
a juxtaposition without inner principle, without coherence, 
without unity. Each stone in such a heap preserves its own 
individuality, and does not unite with the others in realising 
some common purpose. On the other hand, imagine suitable 
stones withdrawn from the heap and put together in such a 
way as to construct an arch-way over a door. Such an arch- 
way is a totality, and possesses a larger individuality of its 
own. If one of the stones is withdrawn the arch is weakened, 
and, on the other hand, by belonging to such a totality, each 
stone partakes in a higher individuality than it possessed by 
itself, an individuality, e. g., with social and aesthetic, as well 
as physical, values. An organised totality is thus a system- 
atic complex of elements, each of which has its own identity, 
and is different from each of its fellow-elements; but the 
differences are not absolute, they are transcended so far as all 
elements are pervaded by one and the same common purpose 
or meaning, some principle which unites them all in the 
service of the whole, and thus gives them a value different 
from, and higher than, that which they possessed apart from 
such organisation. 

Let us apply this to judgment. Take the case #2 — y2 — 
(x+y) (x — y). This is a complex totality, a unity of ele- 
ments such that if one were withdrawn or altered, the equation 
would be radically changed. Exchange, for instance, a plus for 
a minus sign, remove a pair of brackets or the sign of squar- 
ing, and the equation simply vanishes. Consider further the 
elements x and y. Apart from its place in such a judgment, a?, 
for instance, has perhaps, an individuality of its own, as a let- 
ter of the alphabet, which may conceivably be used as an alge- 
braical symbol. Place it in the judgment, and it is at once 
altered by the fringe of relations into which it enters. These 

65 



66 INTERNAL ORGANISATION 

give it a new meaning and value. On the one side of the 
equation it is squared, and 2/2 is subtracted from it; on the 
other side, y is added to it in one bracket, and subtracted from 
it in another, and the complex results are multiplied together. 
Further, both sides of the equation have a certain unity: by 
diverse paths they both lead to one and the same result. Our 
element has thus ceased to be the mere alphabetical x, and has 
become a symbol transferred to do algebraic service, and 
transmuted in the process. It is now steeped in a new color- 
ing derived from its relations to y within the totality which 
is the whole judgment of equality. Furthermore, while x by 
itself is different from y by itself, the unity which is the total 
judgment overcomes and is constituted by the special differ- 
ences of x and y in relation to one another within the equa- 
tion. 

So much for a general example. Let us now turn to the 
special types of judgment, in order to consider the part played 
by organisation somewhat more in detail. 

(A) In Judgments of Perception. — Such a judgment as "This 
room is warm" is a complex totality in which no part could 
be altered without changing the meaning. Let us consider 
the elements out of which it is constructed. As for 8 and P, 
we have already seen that "The room" and "warm" are iden- 
tities, and that they are different identities. It remains to 
see how they are organised with reference to one another, 
how the differences are overcome, and how, within the judg- 
ment, both "The room" and "warm" acquire new and higher 
shades of meaning by uniting to constitute the higher indi- 
viduality which is the total judgment. Consider "The room" 
apart from the judgment. It is a space enclosed by four walls, 
a ceiling, and a floor, and possesses two windows and a door. 
It might be thought of as usable for studying, or for enter- 
taining friends, or for a thousand other purposes. That is 
to say, it might enter into a thousand judgments. But apart 
from judgments of definite kinds, it is not so thought of. It 
is merely "This room." Within the judgment it at once 
receives a new meaning, it is thought of as "warm," i. e., 
in relation to temperature-values as sensed by me, tempera- 
ture-values of which, perhaps, I disapprove, and which it is 
in my power to alter. Similarly "warm" is not thought of as 
warmth-in-general, mere physical warmth, but as the genial 
or unpleasant warmth of this room of mine, a degree of tern- 



IN PERCEPTUAL JUDGMENTS 67 

perature which may make my work comfortable or uncom- 
fortable, may leave me contented, or may lead me to take 
measures to change the temperature. It is plain, then, that 
in the judgment, both "The room" and "warm" have become 
pervaded with new shades of meaning. £ is more than mere 
8, and P is more than mere P. They are now the fif and P 
thought of in relation to one another in a special judgment 
which I make. The organisation of £ and P which is the 
judgment, on the one hand gives them their new meaning. On 
the other, the relations of identity and difference of 8 and P 
within the new totality constitute my judgment of perception. 

Let us push our analysis more into detail, and examine 
further the elements which compose 8. For 8, within the 
judgment, is itself no bare identity, but is a complex, con- 
structed out of a number of different identities. What, then, 
are these elements? Let us consider. In such a judgment as 
"This room is x feet long, y feet broad, and z feet high," 
"The room," as the subject-concept, is constructed out of spa- 
tial elements. In such a judgment, on the other hand, as 
"This room is thoroughly suitable for entertaining friends," the 
subject-concept is constructed out of social elements, or at least 
out of elements which have an especially social reference. 
In the judgment that "This room is warm," again, it is con- 
structed chiefly out of temperature-elements. In other words, 
that which decides just which out of the countless possible 
elements shall be utilised in constructing 8, is the meaning of 
the judgment as a whole. Is the judgment concerned with 
spatial values? Then the ^-elements are spatial. Is it with 
temperature-values that we have to do? Then it is tempera- 
ture-elements which constitute the main feature of S. 

Similarly of the elements which compose the predicate. 
Apart from the judgment, "warm" is usually understood as 
a sensation consequent upon the rapid motion of physical 
particles. The concept "warm" can thus be built up out of 
motion-elements. But in such a judgment as "It is warm at 
noon," time-elements enter into the concept; and in such a 
judgment as "The bath is warm," elements connected with 
water, with washing, etc., enter in. In different judgments, 
then, our predicate-concept is constructed differently. We have 
n oo nday-w&rmth, bath-warmth, Jftts-room-warmth. Just pre- 
cisely which, out of the innumerable possible elements, shall 
be used in constructing our predicate-concept, is thus seen to 



68 INTERNAL ORGANISATION 

depend upon the meaning of the judgment as a whole. In this 
way we come to realise that the judgment as a whole, as an 
organisation, is penetrated with one and the same general 
meaning, through and through, down to the minutest details. 
Not only 8 and P as wholes, but also the elements out of which 
8 and P are constructed, are organised in accordance with the 
principle which gives us a single judgment, an act of thought 
which is one. 

It remains to compare the sensory consciousness with what 
we find when our thought is organised so as to reach the 
intellectual level. At the sensory level, as we have already 
seen, there is a continuous flow of consciousness, without 
distinction or unity, not in any way cut into lengths. Ele- 
ments are placed in this stream in the chance order in which 
they happen to us, without any reference to relevance or con- 
gruity. Thus, if we arbitrarily cut off a section of this stream 
and examine it, we find, e. g., desires for something to eat, 
a wish that it were not so cold, a half-stifled suggestion of 
conscience that we ought to be working, some reverberations 
in consciousness of the last book we have been reading, and 
a thousand other heterogeneous elements of experience, all 
jumbled up together in what, for the intellectual judgment, 
would be hopeless confusion. At the sensory level, however, 
this is appreciated only as a vague richness of life-feeling. 
When this mass of sensory feeling is intellectualised, organ- 
isation, with its tools of identity and difference, has analysed 
out of the mass only such elements as fit in with the plan 
of the judgment, has excluded every element which fails to 
cohere in a single complex meaning, and leaves us with a 
closely organised, coherent system of intellectualised elements, 
each of which is permeated with one thought, and contributes 
to the construction of a complex thought-totality, a judgment 
which is not many, but oneX 

(B) In Judgments of Experience. — Such a judgment as 
"The freight-train disturbances are growing more troublesome 
every year" is a complex totality, in which, if any element 
were omitted or added, some change to the whole would cer- 



i In the above case, and throughout the chapter, we are assuming 
that the intellectual process of organisation is carried out completely, 
and thus really does penetrate down to the details. In actual fact, in 
the rush and hurry of practical life, it is seldom that we have time 
for such patient analysis, and the details tend to be slurred over, to 
an extent which frequently leads us into serious error. 



IN EXPERIENTIAL JUDGMENTS 69 

tainly result. Let us consider the elements which constitute 
this complex, in order to discover what new increments of 
meaning, if any, they acquire by entering into the judgment. 
8 in this judgment is "the freight-train disturbances. " Apart 
from the judgment this might be used in summing up imper- 
sonal, neutral occurrences, a fit subject, e. g., for statistics. 
But the moment such a subject enters into the judgment, the 
moment that such "disturbances" are disturbances of my 
work, and not only so, but are growing icorse, so that I decide 
chat something will really have to be done — S has ceased to be 
an impersonal, neutral entity, and has acquired new shades of 
meaning of a very pronounced kind. Similarly with P. Within 
the judgment, P is no increasing-troublesomeness-in-general 
but is a very specific kind of increasing troublesomeness, a 
freight-train troublesomeness which interferes with my work 
to such an extent that I am goaded into action. $ is no mere 
subject, but the subject-of-this-predicate: and P is no mere 
predicate, but the predicate-of-this-subject. Apart from the 
experiential judgment which brings them together in this 
way, each would, no doubt, possess its own individuality, but 
they would not enter into that larger individuality of the 
judgment, in which they participate in a wider and deeper 
significance, and constitute integral portions of a meaningful 
thought-structure. 

Let us now consider S and P. not so much in their relation 
to the total judgment, as in their character as complexes. For 
the experiential judgment is a summing up of many more 
elementary perceptual experiences, and this characteristic of 
complexity is reflected in the constitution of & and P. In the 
case of fif, it is not difficult to realise what elementary percep- 
tual experiences are therein summed up: the elements are 
clearly single sense-experiences of freight-train disturbances. 
Just what principle governs the selection of these experi- 
ences, we can, perhaps, best realise by comparing a number 
of judgments with the same subject. (1) "The freight-train 
disturbances are, on the whole, a help, a stimulus to better 
work"; (2) "The freight-train disturbances are things of the 
past," (3) "The freight-train disturbances are amply com- 
pensated for by the ease with which we send and receive ship- 
ments." In each of these cases, £ is the disturbance of my 
work due to freight-trains. But in each case it is composed 
of slightly different elements, and has a distinctly different 



70 INTERNAL ORGANISATION 

coloring. In the first case, the disturbance is looked on, not 
as a blank evil, which must be stopped, but as a positive help, 
a "most favorable pause," as the psychologists call it. 8 is 
in this case a complex composed of a series of "most favor- 
able pauses." In the second case, the disturbances to my work 
are over and done with, things of the past, out of practical 
politics once for all. The elements of which 8 is composed are 
here single disturbances, to each of which is appended the 
clearly written label, "Past-and-done-with." In the third case, 
the disturbances to my work are real enough, but the advan- 
tage of having my shipments carried is so much in the fore- 
ground of my consciousness, that I am willing to put up with 
a little disturbance. In this case, the complex 8 is composed 
of a number of freight-train noises, each of which has two 
sides, (a) a disturbing side, (b) an advantageous side which 
at least counterbalances the disturbance. In the case which 
we are especially considering, 8 is composed of a number of 
single train-disturbances, which are thought of as without 
redeeming qualities, as troublesome, and increasingly trouble- 
some, as goading me into action of some sort. On what does 
the difference in the composition of 8 depend, in these vari- 
ous cases? It is not hard, after such comparison, to realise 
that it depends on the judgment as a whole. In making a 
judgment with an eye to "favorable pause," we select from 
the mass of experiences only such as are thoroughly attuned 
to this chord, and can be regarded strictly from that view- 
point. In making a judgment in the light of irritated feelings 
of increasing troublesomeness, we naturally pick out for our 
complex 8, only such elements as are to the point, strictly 
relevant to the issue. In the same way, the elements out of 
which P is constructed depend on the principle of organisa- 
tion which gives us the judgment. Consider the following 
cases: (1) "My increasing correspondence is growing more 
troublesome"; (2) "The management of my increasing income 
is growing more troublesome"; (3) "To have so many atten- 
tive and devoted friends is growing more troublesome." We 
can see at once that the elements out of which the "trouble- 
someness" is constructed, must be distinct in such cases as 
correspondence, management of income, and numerous 
friends. In fact, without further analysis we can, perhaps, 
sufficiently realise that the difference in coloring which thus 
spreads over the elements out of which P is constructed, 



IN EXPERIENTIAL JUDGMENTS 71 

comes from the judgment as a whole. In this way we see 
that, both in the case of 8 and in the case of P, the new 
coloring, the new shade of meaning, passes over, transforms, 
and permeates every detail, in exact proportion as the judg- 
ment is thoroughly organised on one principle. 

We must now compare the judgment as organised, with the 
sensory level of consciousness. At the sensory level, as we 
have seen, our present sense of the train-rumble expands in 
space and time, so as to include in one continuum all similar 
train-rumbles in the past. But it remains to point out that 
this continuum differs sharply from the intellectual organi- 
sation of those same train-rumble experiences. The sensory 
continuum contains these experiences in the same order in 
which they first happened to us. They are not compared and 
summed up. And further: they do not stand out from their 
context, but each is embedded in a tissue of associated experi- 
ence, which clings to the rumble-experience merely because 
it occurred to us at the same place, or in immediate sequence. 
Association by contiguity or succession, as this is technically 
called, is mechanical, unintelligent, blind, a matter of chance 
happening, rather than of rational organisation. Rational 
organisation analyses this mass of associated experiences, 
selects only what is appropriate to the purposes of the judg- 
ment, excludes everything which is irrelevant, and out of 
elements thus chosen for their suitability constructs the com- 
plexes $ and P, in such a way that their relation to one 
another contributes to the unity and significance of the judg- 
ment as a whole. Intellectual organisation, then, penetrates 
down to the minutest details of the experiential judgment, 
and rearranges these in the light of its own principle, or 
main purpose. Only thus do we construct a complex thought- 
totality which has unity, a judgment or act of thought which 
is one. 

(C) In Symbolic Judgments. — Take such a judgment as 
"Rome was occupied by Caesar." That this is a totality, a 
complex which has its own principle of unity, we can at once 
realise if we try to change any of the component elements. 
Let us consider these elements, and see what new shades of 
meaning they acquire by entering into this totality. S for 
instance, apart from this judgment is the city of the seven 
hills, the subject of the various changes recorded in the His- 
tory of Rome. How this differs from the "Rome" of our 



72 INTERNAL ORGANISATION 

judgment, we can perhaps best realise if we compare a num- 
ber of judgments, in each of which "Rome" is the subject. 
E. g. f (1) "Rome is the city of the seven hills"; (2) "Rome 
was the chief seat of the medieval Christian Popes," (3) 
"Rome is the seat of the modern Italian government." In 
none of these cases do we find any of that excitement of panic 
and triumph characteristic of the Rome occupied by Caesar. 
Geographical Rome, Christian or Papal Rome, the Italian 
capital — we at once see that as the judgments differ, into 
which the concept "Rome" enters, so does the concept itself 
differ. In the case especially before us, it is the panic and tri- 
umph, the flight of Pompey and the in-march of Caesar's vet- 
erans, which lend their shades of meaning to the city of the 
seven hills. By entering into such a judgment, the concept 
has acquired a distinctive meaning, new shades of significance 
which it never possessed before. So too of the predicate-con- 
cept. "Occupied by Caesar" has a different significance when 
predicated of Rome, than when predicated of e. g., the various 
cities of Gaul or Spain. These latter-mentioned "occupations" 
were, in a way, legitimate enough: incidents of minor impor- 
tance in wars sanctioned by the conditions of the age. But 
the forcible occupation of Rome by one of her own citizens 
was of major importance, a matter of especial daring, and — 
in spite of precedent — was felt by many to be without pos- 
sible justification. Thus we see that "occupied by Caesar" 
has a different significance in different judgments. In other 
words, the predicate-concept, as well as the subject-concept, 
receives a new coloring, peculiar shades of meaning, from 
the judgment into which it enters. 

If we carry our analysis further, and consider not merely 
8 and P as wholes, but the elements out of which 8 and P are 
made, here again it is not difficult to realise that these two 
are permeated with the meaning of the judgment into which 
they enter. In every symbolic judgment, as we have seen, 
the elements out of which we construct, for example, our 
^-concept, are drawn from our own experience, and selected 
and arranged in order to meet the requirements of the spe- 
cial case. In Rome as the city of the seven hills, the elements 
from which we construct the ^-concept are experiences of 
hills, geographical experiences. In the second case, the ele- 
ments are peaceful, Christian experiences, suited to the milder, 
more religious and venerable aspects of Church history. In 



IN SYMBOLIC JUDGMENTS 73 

the third case, it is elements connected with the aspiration 
for liberty and unification — associated wijth the names of 
Garibaldi, Victor Immanuel, and Humbert, — on which we 
draw. In the Rome occupied by Caesar, on the other hand, 
it is, as we have already seen, elements of panic and triumph, 
which we tear from their contexts in our personal history 
and reconstruct in such a way as to feel something as a 
Roman citizen might have felt under the circumstances. That 
is to say, in selecting the elements out of which to construct 
our ^-concept, we are governed strictly by the judgment as a 
whole, and accept only such elements as are relevant to the 
general meaning of that judgment. 

So too with the elements out of which P is constructed. 
"Occupied by Caesar" has, as we have seen, different shades 
of meaning in different judgments. From our present stand- 
point, this means that the elements which we take from our 
own experiences and re-arrange so as to realise the meaning 
of our concept, differ when the meaning is different. When 
it is some Gallic town which is occupied by Caesar, we do 
not select feelings appropriate to the occupation of the great- 
est city of the then world, which was at the same time 
Caesar's own mother-city. Thus we see that, in every detail 
of the judgment, in the elements of which S and P are made 
up, as well as in the case of S and P taken as wholes, as units, 
the principle which governs the selection of materials, and 
decides what shall be used and what rejected, is the meaning 
of the judgment as a whole, the principle of organisation 
which makes it one complex, a totality. 

Finally, we must compare the organised symbolic judgment 
with the sensory level from which it has arisen, the level at 
which our eye appreciates the form and position of the let- 
ters, and our hand turns over the pages, but our minds fail 
to grasp and hold fast the further meaning of the symbols 
in our printed book. At the sensory level, our consciousness 
flows evenly along, without a ripple disturbing the serenity 
of its surface, blissfully unaware of the tragedies of Roman 
life and the ascendency of Caesar's star. Intellectual organ- 
isation of this stream of consciousness occurs when we arrest 
the flow of this stream in order to stop and think. We look 
before and after, combine the letters into words, the words 
into the unity of apprehended sentences, of judgments in 
which the symbols are realised in terms of re-organisations 



74 INTERNAL ORGANISATION 

of associated experiences. It is like what happens in the 
experiential judgment, but with this difference, that the 
organised result represents no mere summing up of our own 
experiences, but goes further. It consists of an organisation 
of experienced elements which approximate to, and are used 
to stand for, an experience we have never had, the experience 
of a citizen of Rome during the time of its occupation by 
Caesar. Our intellectual organisation penetrates down to the 
minutest elements of our thought, the fragmentary experi- 
ences which we put together in order to realise what is meant 
by 8 and P, and every element in the judgment, so far as 
it is intellectually organised, is penetrated through and 
through with one and the same complex meaning, in such a 
way as to give us an act of thought which, though complex, 
is single, a judgment which is one. 

(D) In Transcendent Judgments. — Such a judgment as 
"God is a substance with infinite attributes" is an organised 
totality, i. e., is such that if a single element (e. g., one of 
the Divine attributes) were taken away, the meaning would 
be radically altered. Let us consider these elements. As 
belonging to an organised whole, they mu,st be altered by 
participating in it. Consider 8. Apart from the judgment, 
"God" might mean, e. g., the ideal of a Perfect Self to which 
we aspire. God as the goal of aspiration differs sharply from 
God as a "substance with infinite attributes." The warm, 
personal shades of meaning associated with human aspira- 
tion are lost in the impersonal, mathematical relation of 
attributes so many as to transcend all human qualities what- 
ever. The concept of God has now acquired the "eternal" 
or timeless aspect which we attribute to mathematical entities, 
and the chill remoteness of this highly intellectual fringe of 
meaning has altered our concept almost beyond recognition — 
at least, for all who have not yet learnt to consider ideas 
sub specie aeternitatis. Similarly the predicate-concept "sub- 
stance with infinite attributes" — in itself a wholly colorless 
quasi-mathematical entity — acquires by being associated in 
one and the same act of thought with "God"-— the object of 
reverence and aspiration — something at least of the warmth 
and intimacy of personal feeling, a shade of meaning which 
connects it with human life. Thus we see that both 8 and P 
receive new and valuable elements of meaning by entering 



IN TRANSCENDENT JUDGMENTS 75 

into the intellectual organisation which is the transcendent 
judgment. 

Let us consider further the elements which together con- 
stitute the complex 8 and the complex P. These elements are, 
of course, selected as being suitable to form 8 and P. But if 
the standard of organisation has been thoroughly introduced 
into the judgment, we should expect only those elements to 
have been selected which are appropriate to the special mean- 
ing of this & and this P in our organised judgment. Let us 
consider whether this is, in fact, the case with 8. Are the 
elements which constitute the concept of God the same in 
such judgments as "God is the all-knowing, all-powerful 
creator of the world," "God is the ideal spiritual life in which 
we live and move and have our being," and "God is a sub- 
stance with infinite attributes?" A little attention suffices 
to convince us that the component elements of the God-con- 
cept are different in each of these judgments. In the first, 
God is thought of as composed of elements of knowledge and 
power suitable to the world-creator, magnificent, wonderful, 
the subject of admiration and perhaps fear. In the second, 
God is thought of as life at its best, the kind of life of which 
we catch faint glimpses in our most exalted moments, and 
the component elements of the concept are precisely these 
moments of life in which we are at our best. In the third, 
the elements which together constitute the concept are the 
different attributes, extension, thought, and an infinity of 
others, each one of which is magnified to infinity. As far as £ 
is concerned, then, it appears that its constituent elements 
have been selected in accordance with the meaning of the judg- 
ment as a whole. 

So too of the elements which together make up the predi- 
cate-concept. Extension and thought, as attributes within our 
human experience, are imperfect and finite. But as attrib- 
utes of a substance which is not human but Divine, they 
are at once altered to fit the new case. We piece out their 
imperfections with our thoughts, and try to conceive them 
as perfect, or, as Spinoza expresses it, "infinite." Further, 
we human beings know only the two attributes of extension 
and thought. But when we wish to build up the idea of a 
substance which is God, we postulate an infinity of other 
attributes, of which we have not the faintest positive idea, 
but only the persuasion that they must be added as necessary 



76 INTERNAL ORGANISATION 

elements in the absolutely perfect Being. For this is to be 
without limitations or wants, and transcends the best that 
we human beings know, not only in quality, but also in quan- 
tity. In this way, then, we see that the introduction of the 
standard of complete intellectual organisation affects not only 
the # and P of our transcendent judgment considered as 
wholes, but also the minutest details among their component 
elements. 

It remains to compare the transcendent judgment as a 
whole with the sensory consciousness from which it has 
arisen. At the sensory level we have a vague general aware- 
ness, without precise limits, which contains in the germ the 
feeling of helplessness and dependence, as well as countless 
impulses, sensations, and feelings of all sorts. On the limpid 
surface of this broad stream, larger ripples come and go; but 
they are lost in the general motion of the stream, and nowhere 
do we find sharp outlines, clear-cut distinctions. All is con- 
tinuous, even, placid. In comparison with this sensory level, 
the introduction of organisation which results in the trans- 
cendent judgment stands out in the greatest possible contrast. 
It is all lines and angles, discontinuities, sharply differenti- 
ated identities. The stream of consciousness has been split 
up into innumerable distinct elements. The hundred and one 
elements which are irrelevant to the conception of God as a 
substance — e. g., the sensations and impulses arising from the 
chance sounds and sights of the external world — are sifted 
out and excluded from the judgment. On the other hand, 
all elements which are strictly relevant — such as feelings of 
helplessness and human dependence — are retained, and not 
merely retained, but retained in a very special form. They 
are differentiated and identified, cleared of every vestige of 
irrelevance, purified of the particular accidents of their sen- 
sory contexts, brightly polished until they are fit to take 
their place in the new system— a system characterised by 
intellectual clearness, coherence of meaning, unity of plan. 
In place, then, of a stream of sensory waves bound together 
merely by the continuity of happening, we have a system of 
intellectualised elements distinguished and held over against 
one another in a unity which is bound together by identity 
of reference, relevance, meaning. 

Conclusion — The Function of Organisation. — If we now put 
together the results reached in considering the various types 



FUNCTION OF ORGANISATION 77 

of judgment, perceptual, experiential, symbolic, and transcen- 
dent — we see that organisation makes itself felt by uniting 
diverse identities in the service of one common purpose or 
meaning. We see this especially in three ways: (1) With 
reference to 8 and P. These are diverse identities. Apart 
from the organisation which brings them together, each has 
its own individuality and meaning. But when organised, 
with reference to each other, in a single act of thought, each 
acquires a new significance by partaking of a common mean- 
ing, which is wider and deeper than either possessed by itself. 

(2) The elements which together make up 8 and P are 
similarly influenced and transformed, down to their minutest 
details, by entering into the organised judgment. According 
to the meaning of the judgment, some of the possible elements 
are sifted out and rejected, while others are taken up and 
joined together in the service of the new judgment which 
makes them partakers of its own meaning. That is to say, 
only such elements are selected as are suitable to form, not 
&-in-general or P-in-general, but the £-in-relation-to-P, and 
the P-in-relation-to-#, in the unity of the new act of thought. 

(3) Finally, by comparison with the sensory consciousness, 
we discover that, while at the sensory level the different com- 
ponent elements of the conscious stream are held together by 
continuity, in the order in which they have happened to 
us — at the intellectual level, the articulate system of elements 
in which the organised judgment consists is held together 
by identity of reference and unity of meaning. 

FOR FURTHER READING 

J. G. Hibben, Logic, Part I, chapter xi. Chr. Sigwart, Logic, Vol. 
II, pp. 144-158. 

EXERCISES 

1. What are &. P. and their respective elements, and how are 
they affected by being brought together in the following judgments : 
These beets taste excellent. This overcoat is too heavy. That dark 
patch is slippery? 

2. What are & 3 P, and their respective elements, and how are they 
affected by being brought together in the following judgments : I have 
found shorthand useful in my work. The business section of the 
town has been expanding in the last few years. Spinach has proved 
unsatisfactory as a garden vegetable — at least in my experience. 

3. What are S. P 3 and their respective elements, and how are they 



78 INTERNAL ORGANISATION 

affected by being brought together in the following judgments : Hon- 
esty is the best policy. The sources upon which Tacitus relied in 
writing his Annals were prejudiced. A life spent without reflection — 
without taking stock of one's powers and critically deciding upon a 
plan of action — ds no life at all? 

4. What are S, P, and their respective elements, and how are 
they affected by being brought together in the following judgments : 
What must be, and may be, assuredly is. With God, all things are 
possible. I have invented a motor which will generate its own motive 
power, and thus go on for ever. 



CHAPTER VIII 
ORGANISATION, (B) EXTERNAL 

The Introduction of External Organisation. — Let us con- 
sider what we already know about organisation. The minut- 
est elements of our thought are organised from the viewpoint 
of some wider unity, which is 8 or P. £ and P in turn are 
organised from the viewpoint of some wider unity, which is 
the judgment. Can we continue, can we regard judgments 
also as organised from the viewpoint of some yet wider 
unity? S and P, for instance, have two kinds of organisa- 
tion. (1) In reference to their constituent elements, they 
are internally organised. (2) In reference to the judgment 
as a whole, they are externally organised. In the same way, 
the minutest elements are externally organised in reference 
to S and P, or to the judgment as a whole. The judgment as 
a whole, however, has been so far considered only in refer- 
ence to its constituent elements, i. e., as internally organised. 
In the present chapter we must attempt to discover whether 
it has external organisation also, and, if so, what part this 
plays in our thought. 

Take, for example, the judgment "7+5=12." This is inter- 
nally organised in reference to the units which constitute the 
judgment. But the matter does not stop here. Each arith- 
metical judgment is not a unity with internal organisation 
only, standing, in splendid isolation, aloof from all other 
judgments. Arithmetical judgments hang together, cohere 
in one system of meaning. 12, for instance, can be reached 
by other equations, such as 20 — 8, 4X3, 48-^4, etc., and these 
different judgments belong together in such a way that we 
can say e. g., "7+5=20—8=4X3=48-^-4=12." They belong 
together in virtue of the fact that they are externally organ- 
ised in reference to one and the same arithmetical series, 1, 
2, 3, . . . and represent the internal organisation of this 
series. So too geometrical judgments cohere in one system, 
being externally organised in reference to space, plane geo- 
metry to a space of two dimensions, solid geometry to a 

79 



80 EXTERNAL ORGANISATION 

space of three dimensions, and "metageometry" to a space of 
n dimensions. Similarly algebraical judgments belong to 
a single system, and if we pass to the more empirical sciences 
of physics, chemistry, biology, psychology, etc., we must 
recognise here also, that each of these sciences consists of 
a group of more or less coherent judgments. 

But the matter does not stop even here. These various 
groups, arithmetic, psychology, physics, etc., are organised 
still further in reference to one another, or perhaps to a 
wider unity to which all alike belong. Many problems, for 
instance, can be solved indifferently by arithmetic, algebra, 
or geometry. New discoveries in physics or chemistry shed 
light on dark places in botany, psychology, etc., and all the 
natural sciences make much use of mathematical equations. 
This universal use of mathematics shows that the various 
scientific thought-structures have at least one common factor. 
When we further reflect that biology, psychology, physics, 
etc., deal with relations of cause and effect, while all sciences 
whatever deal with relations of ground and consequent and 
other logical relations — i. e., where all sciences make use of 
logic and mathematics, they must be, to that extent at least, 
interrelated, must form parts of a wider whole which is at 
least partially organised. From this we can, perhaps, realise 
that all judgments whatever are, at least ideally, interrelated, 
and all belong to the vast body of organised, or ideally organ- 
isable, knowledge. 

The ideal of knowledge is thus a vast system in which all 
possible discoveries in the departmental sciences might be 
completely organised in reference to one another. The system 
is internally organised in the form of the special sciences, and 
conversely, the various judgments which compose the special 
sciences can be regarded as externally organised in reference 
to this system of possible knowledge, and thus as being sub- 
ject to the demands of consistency within a system which is 
one. The unity of the thinkable is thus the ultimate intel- 
lectual principle, in reference to which all judgments are 
externally organised, or at least externally organisable. In 
actual practice, in the hurry and rush of our every-day con- 
cerns, few, even scientists, push their researches to this length. 
They tend to remain content with an external organisation 
v/hich merely gives the fringe or general setting of their 
special science; but it is always understood that such results 



IN PERCEPTUAL JUDGMENTS 81 

are provisional merely, until they have been worked over 
and transformed from a deeper viewpoint.! Then only are 
they fit to take their position in the ideal system which is 
Truth. 

So far, then, we have seen that judgments are externally 
organised (a) in reference to the special department of knowl- 
edge within which they fall, and (b) in reference to the ideal 
unity of what can be thought consistently. Let us con- 
sider the meaning and value of this for the special types of 
judgment. 

(A) In Judgments of Perception. — Take such a judgment 
as "This room is warm." In the sense in which we have 
hitherto understood it, this judgment falls into at least the 
following departments of knowledge: (1) temperature-judg- 
ments, (2) sense-judgments, (3) practical judgments, (4) 
psycho-physical judgments with a background of nervous 
physiology, leading to (5) chemical and (6) physical judg- 
ments, with all which these, in their turn, also imply. Ulti- 
mately, it belongs to (7) the class of "thinkables," i. e., judg- 
ments intellectually organised in the systematic unity which 
contains every possible thought. 

Let us consider, then, for the perceptual judgment, what 
is the meaning and value of its external organisation In 
respect of these various classes. For example, the tempera- 
ture class consists of judgments like "This is cool," "This 
is warm," "This is just right." That is, it is internally 
organised into a number of precise judgments which, taken 
together, contain the whole meaning of the temperature class. 
If any one of these judgments is taken apart from its mem- 
bership is such a class, it has, no doubt, some faint meaning 
of its own, but it loses all connection and contrast with the 
other judgments within the group, and it is just the extra 
fringe of meaning given by membership within the group 
which makes the judgment significant. "This room is warm." 
Taken as an isolated fragment of thinking, apart from the 
class of temperature-judgments, i. e., apart from any contrast 
with the temperature which is "cool" and the temperature 
which is "just right," such a judgment has almost no signifi- 
cance. It is only by becoming a member of such a class that 



i Cf. e. g., Groos, The Play of Animals, B. T. 1911, pp. 30-31, and 
A. E. Taylor, Elements of Metaphysics, 1903, pp. 3-5. 



82 EXTERNAL ORGANISATION 

it ceases to be an abstraction, an isolated fragment, and con- 
stitutes a vital portion of our concrete thinking. Thus we 
see that the external organisation of "This room is warm" 
in terms of temperature-judgments is an integral part of the 
wider meaning of our thought. 

So too with the other departments of knowledge within 
which our perceptual judgment falls. E. g., the class of 
"practical" judgments consists of thoughts which have a 
clear connection with advantageous action, i. e., which lead 
to such action. If our judgment concerning the warmth of 
the room is not a member of this class, it can have only a 
contemplative significance, divorced from action. It is only 
so far as my thought is externally organised with reference 
to action that I rise and attend to the furnace, for example, 
or take precautions against an outbreak of fire; and the prac- 
tical value of such connection with such action speaks for 
itself. The practical element, then, constitutes an integral 
portion of the wider meaning of our perceptual judgment. 

It remains to ask what difference membership in this exter- 
nal context makes to the judgment itself. Are the elements, 
for instance, out of which the judgment is constructed, in 
any way altered as our judgment enters into some wider class? 
Does the organisation which we have called external remain 
merely external, or does it penetrate even into the internal 
construction of the judgment, and into the elements out of 
which 8 and P are built up? 

There can be no doubt as to our answer. We have already 
seen that the internal organisation is dependent on the gen- 
eral meaning of the judgment, and that the meaning of the 
judgment alters according as we regard it on the one hand 
as an isolated fragment of thinking, or on the other as a mem- 
ber of some definite class, i. e., as externally organised in 
some wider intellectual context. For instance, if "This room 
is warm" be regarded (1) as a member of the class of prac- 
tical judgments, and (2) as not a member of such a class, 
there can be no doubt that the connection with action — or 
severance from action, as the case may be — enters into the 
selection of elements out of which S, P, and the whole judg- 
ment are built up. In the first case, most of the temperature- 
values selected will be connected with well defined actions. 
Elements of "just-rightness," for instance, are associated with 
sitting still; elements of "coolness" or "warmth" are asso- 



IN PERCEPTUAL JUDGMENTS 83 

ciated with diverse operations upon the thermostat or directly 
upon the furnace. In the second case, on the other hand, every 
element is carefully divorced from its customary association 
with action, and is regarded in a rigidly speculative light. In 
this way we see that the selection of elements out of which 
the judgment is composed, is governed not only by (1) the 
meaning of 8 and P and (2) the meaning of the judgment as a 
whole, but also by (3) the wider meaning of the intellectual 
context into which the judgment enters. Hence we conclude 
that, just as S and P are externally organised in the wider 
totality which is the judgment, so the perceptual judgment is 
externally organised in the wider totality which is its intel- 
lectual context. 

(B) In Judgments of Experience. — Take such a judgment as 
"The freight-trains crossing the bridge are becoming yearly 
more troublesome." In the sense in which we have under- 
stood it previously, this judgment falls into at least the fol- 
lowing departments of knowledge: — (1) judgments based on 
sense-perception, (2) practical judgments, and — in the wider 
field of implication — (3) social judgments, (4) physical judg- 
ments, etc. Finally it falls into the class of "thinkables" or 
intelligent judgments thought of as forming a single coherent 
system. Experiential judgments are thus externally organ- 
ised in much the same way as we have found to be the case 
with perceptual judgments. 

Let us proceed to ask what difference it makes to an expe- 
riential judgment, to be externally organised in this kind of 
way. Hitherto we have regarded our example of an experi- 
ential judgment as falling predominantly within the class of 
sense-judgments. It is emphatically the noise made by the 
trains which is such a disturbing element, and the judgment 
as a whole is a summing up of such noise-disturbances, such 
offences to our ear. The sensory element is thus very pro- 
nounced. If, now, we think of it apart from membership in 
such a class, if we think away the noisiness of the freight- 
trains, they have also lost their disturbing character — in other 
words, the characteristic meaning of the judgment has van- 
ished. Our thought is thus dependent on such external organ- 
isation for the significance which it has for us, and member- 
ship in this class is a legitimate part of the wider meaning 
of the experiential judgment. 

So too with the other classes in reference to which our judg- 



84 EXTERNAL ORGANISATION 

ment is externally organised. Consider, for example, the prac- 
tical and social classes. In the sense in which we have taken 
it hitherto, our judgment about the train-disturbances is no 
impersonal, contemplative summing up of evidence. The dis- 
turbances interfere with our work, and to such an extent that 
we are impelled to do something about them, to write to some- 
one, to organise social pressure and bring it to bear, etc. 
Deprive the judgment of its external organisation in these 
classes, and you destroy a large part of its significance for us. 
Thus we realise that here also, the practical and social ele- 
ments constitute a legitimate portion of the wider meaning 
of our judgment of experience. 

The same is the case with all the classes into which our 
judgments of experience undoubtedly fall, and our general 
conclusion inevitably is, that such judgments are not com- 
plete, if we regard them as units to be taken by themselves; 
on the contrary, each judgment of this kind enters into a 
wider intellectual context in which it obtains most of the ele- 
ments of meaning which make it valuable and significant 
for us. 

It remains to ask whether this external context is merely 
external, or whether, as we found to be the case with per- 
ceptual judgments, it enters also into the internal structure of 
the judgment. Do 8 and P, and the elements out of which 
these are put together, remain constant, unaltered, however 
their intellectual context may vary, or are some elements sifted 
out and rejected, while others are selected and retained, accord- 
ing as the guiding-thread of the external organisation directs? 
There can be no doubt about our answer. What governs the 
selection is, as we have seen, the meaning of the judgment as 
a whole, and the meaning of the judgment as a whole varies in 
accordance with the intellectual context into which it enters. 
Hence the elements selected in the construction of 8 and P, 
and of the judgment as a whole, will vary as the wider intel- 
lectual context varies. For example, if the wider context 
demands practical and social action in order to put a stop to 
these noises which interfere with my work, then that aspect 
of each of the recalled train-disturbances becomes selected in 
which the practical and social importance of putting a stop 
to such disturbances is prominent. If, on the other hand, the 
wider context assures us that steps have been taken which 
will prevent a repetition of the disturbances, then each of the 



IN SYMBOLIC JUDGMENTS 85 

recalled train-noises comes before us with the special label 
"over-and-done-with." Thus we see that, in the judgment of 
experience also, the internal organisation is through and 
through dependent on the external organisation. 

(C) In Symbolic Judgments. — Take such a judgment as 
"Rome was occupied by Caesar." In the sense in which we 
have understood it hitherto, this judgment falls into at least 
the following classes: — (1) dramatic, even tragic, judgments, 
(2) historical judgments, with all which these, in turn, imply, 
— e. g., (3) archeological judgments, (4) epigraphical judg- 
ments, (5) linguistic judgments, etc. Ultimately, as history 
occupies a certain place among the sciences, it belongs to the 
system of knowledge, or what we have called "thinkables," 
regarded as an organic totality.2 

What difference does such external organisation make to 
the symbolic judgment? Let us consider. In the sense in 
which we have always taken it, the occupation of Rome by 
Caesar is a dramatic event, an event of even tragical signifi- 
cance. On the one side we have the Pompeians, the Senatorial 
party, representing law and order, the majesty of Rome. On 
the other side we have the "populares," a mixed set of ruined 
and turbulent citizens, led by Caesar at the head of his Gallic 
War veterans, invading their Mother-country. It looks like 
the clash of Might against Right, and the uncertainty as to 
which party and which leader is in the right adds to the com- 
plex dramatic nature of the situation. Deprive the judgment 
of the external organisation in virtue of which it becomes a 
member of this class, and it pales into insignificance. Remove 
the dramatic element, and the meaning dwindles away to a 
mere nothing, a common-place event of no interest-compelling 
importance. In this way we realise that external organisation 
in terms of the dramatic is part of the wider meaning of our 
judgment. It is only when we envisage it as a great step in 
a fateful drama that we appreciate its full significance. 

As with the class of dramatic judgments, so also with the 
other elements in the external organisation which constitutes 
the intellectual context of our judgment. Abstract from this 
context e. g., the historical significance of the judgment, cut 
off our judgment from the evidence of archeology, from its 
dependence on ancient manuscripts, etc., and it becomes at 

2 A. L. Jones, Logic, pp. 266 ff. 



86 EXTERNAL ORGANISATION 

once a very different thing. Events conceived as unhistorical, 
e. g., in works of professed fiction, may have dramatic signifi- 
cance, but our attitude towards fictitious events is sharply dis- 
tinguished from our attitude towards events regarded as his- 
torical, and to relegate our judgment to the fictitious class 
would be seriously to curtail its legitimate meaning. In this 
way we realise that the symbolic judgment cannot be treated 
as a self-sufficient unit, existing by itself in splendid isolation 
from all other judgments, but that it is essentially an organic 
portion of a wide intellectual context which endows it with 
the dramatic, historical, and other elements of meaning which 
make it valuable and significant for us. It is thus externally 
organised in reference to wider universes of meaning, and 
ultimately in reference to, and dependence on, the totality of 
meanings, the system of thinkables, within which historical 
and dramatic judgments have their specific places. 

As in the case of perceptual and experiential judgments, we 
must now ask whether this external organisation remains 
merely external. Does it merely affect the judgment as a 
whole, or does it enter into the internal organisation also, and 
modify the details of the judgment? As we have seen, S, P, 
and the judgment as a whole are built up out of elementary 
experiences; our question thus means, Are these elements 
Independent of the external organisation, do they remain con- 
stant, however the external context may vary — or does the 
external context modify them down to their minutest details? 
Let us consider. The elements used in constructing, our judg- 
ment are such stuff as dreams are made of, as well as sober 
history: — experiences of sunny skies, of crowds, of panic and 
triumph, and so forth, called up by association with the words 
"Rome," "was," "occupied," "by," "Caesar." Of these possible 
associates, as we have already seen, only such are selected as 
are compatible with the meaning of the judgment as a whole. 
That is to say, the associates called up by each word are pro- 
foundly modified by their connection with the associates of 
the other words which together go to build up the complex 
internal structure of the judgment. Are these elements fur- 
ther modified by the entrance of the judgment into a wider 
class? Does it make any difference to the associates selected, 
if the judgment is regarded as fictitious or as historical, as 
dramatic or as commonplace? There can be no doubt as to 
our answer. If the judgment is dramatic and tragic, we cer- 



IN SYMBOLIC JUDGMENTS 87 

tainly tend to select such elements of our crowd-experiences, 
of our panic and triumph-experiences, etc., as are connected 
for us with the dramatic and tragic. If, on the other hand, 
the judgment is regarded as commonplace, we select mainly 
such elements of our crowd-experiences, etc., as are connected 
with every-day feelings. Thus we see that the external con- 
text into which the judgment enters, profoundly modifies the 
details of internal organisation, and in fact, that the construc- 
tion which gives us the symbolic judgment varies as the exter- 
nal organisation varies, or, as we have seen in the previous 
judgment-types, the internal organisation is through and 
through dependent on the wider intellectual context.3 

(D) In Transcendent Judgments. — Consider such a judg- 
ment as "God is a substance with infinite attributes." In the 
sense in which we have understood it hitherto, i. e., taken 
ideally, as realising all which it attempts to accomplish, such 
a judgment can not be said to fall into any larger, wider, more 
inclusive class. It is formed by taking various attributes, such 
as extension and thought, and expanding these to infinity, and 
as the resulting concept of God is explicitly all-inclusive — 
including not only all humanly possible experience, but also 
all possible experience in general, human, angelic, and Divine 
— it embraces already, in its internal context, every universe 
of meaning. There thus remains nothing outside, in refer- 
ence to which it could be said to be "externally" organised. In 
other words, transcendent judgments, taken ideally, are co- 
extensive with the ultimate class, the class of thinkables. 

It should, however, be clear from the nature of the case, 
that a judgment which really and in actual fact was all-in- 
clusive, and embraced in the unity of a single act of thought 
not only all humanly possible experience, but also an infinity 
of experiences of which human beings cannot even frame a 
clear positive concept — i. e., a judgment which really tran- 
scends human experience — cannot be made by a human being. 
In other words, it is only ideally that a transcendent judg- 
ment can be said to have no external context. In actual prac- 

3 Of . W. B. Pillsbury. Fundamentals of Psychology, 1917. p. 340: 
"The outlines of black and white that constitute the words start the 
association processes which lead to the ideas, and these associates are 
controlled by the wider setting and wider knowledge of the individual 
at the moment. . . . The revival of the earlier experiences is 
controlled by the laws of association and by the context in a degree 
that practically OAixounts in many cases to new construction." (Italics 
mine. ) 



88 EXTERNAL ORGANISATION 

tice, the attempts to think metaphysically tend to be one- 
sided, largely formal, finite, and imperfect. They are, in fact, 
symbolic extensions of experience, labeled with the formal 
demand that they should be extended to infinity. But this 
demand remains purely formal, and expresses an ideal which 
we cannot realise in actual concrete thinking. In the case 
before us, for example, we think of God as possessing attrib- 
utes which come within the realm of human experience. 
When we attempt to magnify each of these attributes beyond 
the scope of possible human experience, i. e., to infinity, we 
tend to lose ourselves. For in infinity, in that which is pre- 
sumed to lie beyond human experience, the distinctions which 
have meaning and value within our experience cease to apply. 
Infinite space, for example, cannot be measured out in inches 
or centimetres; infinite time is hopelessly incommensurable 
with our minutes and hours; and the infinite spirituality of 
the Divine cannot be expressed in terms of finite propositions 
taken from empirical psychology. The symbolic ideal of a 
better Self, that is, a Self better than our actual Self, but dis- 
tinctly conceived as within the range of human possibility, 
has meaning and value for the direction of our lives. But the 
transcendent concept of an absolutely perfect Self, a Self which 
transcends infinitely the possibility of human realisation, is so 
remote that we cannot even form a clear positive conception 
of what it means; and its value for our lives diminishes in 
direct proportion to its remoteness.4 

In dealing, then, with actual judgments of this group, we 
may treat them as a slightly more extensive kind of symbolic 
judgment; in which case, all that we have found true of the 
symbolic judgment will hold good here also. If these judg- 
ments are one-sided and imperfect, then it is possible for 
them to have an external context: and if they have an exter- 
nal context, then the general meaning of the judgment will 
alter according to the external context into which it enters. 
For example, if we think of God chiefly as a merciful judge 
of the weaknesses of humanity — i. e., in reference to the class 
"merciful judges" — our thought acquires shades of meaning 
which differentiate it sharply from the thought of God in some 
other context, e. g., as the object of mystical enjoyment, that 
experience of infinite unity in which we are alone with the 

* Cf. H. Sidgwick, Methods of Ethics, pp. 18-22. 



IN TRANSCENDENT JUDGMENTS 89 

Alone.5 In the same way, so far as we regard judgments of 
this group as essentially and in fact extended symbolic judg- 
ments, the external organisation will enter into the internal 
structure of the judgment, and will govern the selection of the 
elements out of which S, P, and the judgment as a whole are 
built up. In other words, transcendent judgments, as actually 
judged by haman beings, are dependent, as to their internal 
organisation, down to the minutest details, upon the wider 
class within which they fall, and this class is ultimately the 
class of thinkables, the ideally complete organisation of all 
which can consistently be thought. 

Conclusion — The Ultimate Intellectual Standard. — If we 
now put together what we have discovered about the meaning 
of external organisation for the various types of judgment, 
certain conclusions stand out with especial prominence. 
First and foremost, no judgment whatever stands by itself, 
but each is an integral portion of some wider universe of 
meaning, which constitutes its intellectual context. Per- 
ceptual judgments are portions of a concrete texture of thought 
which is by no means confined to the perceptual level. This 
intellectual context embraces, as we have seen, not only per- 
ceptual, sensory, judgments, but also summings up of these in 
classified form — i. e., is continuous with experiential and sym- 
bolic judgments. Ultimately, as extending into the field of 
"thinkables," it is continuous with the intellectual context of 
transcendent judgments. Judgments of experience are simi- 
larly portions of a wider context which on the one side forms 
part of our popular, perceptual thought, and on the other is 
intellectually continuous with those summings up of experi- 
ence out of which science is born. Ultimately, as being con- 
tinuous with the texture of science, this intellectual context 
is continuous with the symbolic extension of experience which 
reaches out after infinity and is called transcendent. So too 
the intellectual context of symbolic judgments is on the one 
side experiential, and, on the other, transcendent, while tran- 
scendent judgments seem partly to be symbolic, partly to 
belong to an all-inclusive universe of meaning. Every judg- 
ment, then, is part of a wide system of meaning, which extends 
with unbroken intellectual continuity in the direction of what 
we have called transcendent thinking. 

5 Cf . Plotinus, Enneads, Bk. VI, chapter ix, sec. 10 (in Bakeweli, 
Source Book in Ancient Philosophy, p. 393). 



90 EXTERNAL ORGANISATION 

Let us ask further, are the systems of meaning to which 
different judgments belong, themselves different? For exam- 
ple, does "The room is warm" belong to a different universe 
of meaning, a wholly different intellectual context, from that 
into which such judgments enter as "Rome was occupied by 
Caesar," or "God is a substance with infinite attributes?" Our 
answer must be, No. They belong, of course, to distinguish- 
able systems of meaning, as sense-judgments can be distin- 
guished from historical judgments, or as a judgment based 
on the warmth which we perceive with our senses can be dis- 
tinguished from a judgment about God, whom we do not per- 
ceive with our senses. But these systems are only relatively 
distinguishable — they are not absolutely severed from one 
another. Ultimately all form parts of one and the same great 
system. In the case of the special sciences, for instance, we 
saw that a thread of mathematical and logical thinking runs 
through and so far connects and unifies most of our concrete 
thinking. If we apply this to the present case, we can see 
that all systems of meaning, however diverse in appearance, 
are at one at least in this, viz., that they are all alike systems 
of meaning, that logical thought and intelligible significance 
enters into them all — in a word, that they one and all belong 
to the widest and ultimate totality of "intelligibles" or "think- 
ables." In this way we come to realise that the ultimate sys- 
tem, the circle of widest meaning to which our judgments can 
possibly belong, whether they are perceptual, experiential, 
symbolic, or transcendent, is the totality of thinkables, and 
that in an ideally complete intellectual organisation of our 
sensory consciousness, the various elements which go to form 
the 8 and P of our judgments — "the room," "freight-train-dis- 
turbances," "Rome," and "God," — and indeed every judgment 
of whatever type, must be rational, comprehensible, and think- 
able through and through, so as to be fit without further trans- 
formation, to take their place in a completely intellectualised 
experience, in which all elements whatever would be clearly 
interrelated, and be organic through and through with mean- 
ing^ 

Our final conclusion, then, concerning the intellectual ele- 
ment in judgment is this: — The standards of identity and 



6 Cf. Plato's ideal of Dialectic, as developed in Republic, Bk. VI, 
ad fin., and F. H. Bradley, Principles of Logic, pp. 449-451. 



ULTIMATE INTELLECTUAL STANDARD 91 

diversity or difference are subordinate concepts within the 
wider conception of organisation, and the standard of internal 
organisation is subordinate to the conception of external organ- 
isation. The unity of whatever can be consistently thought as 
belonging to a single intellectual system is, then, the ultimate 
standard of the intellectual side of judgment. It remains to 
inquire into its validity.? 



7 This ultimate standard is what Kant calls the Unity of Self- 
consciousness — i. e., of a single ultimate experience. Kant sometimes 
calls it the "transcendental unity of apperception." Cf. Critique of 
Pure Reason, tr. Meikeljohn, pp. 82—86. Cf. also Bosanquet, Logic, 
Vol. I, p. 144 : "The course of judgment within the present whole 
of perception is determined by connections which refer beyond that 
accidental whole, to other more comprehensive totalities, and ulti- 
mately, in every case, to the system of the known world. The connec- 
tions thus prescribed between part and part within some systematic 
whole are necessary connections." 

FOR FURTHER READING 

B. Bosanquet, Logic, Vol. I, pp. 72-92. W. B-. Pillsbury, The 
Fundamentals of Psychology, pp. 335-344. Chr. Sigwart, Logic, Vol. 
II, pp. 508-528. 

EXERCISES 

1. What is the wider intellectual context of the following judg- 
ments, and now far does It enter into their internal organisation : 
The ice looks slippery. These skates feel sharp. This key is rusty? 

2. What is the wider intellectual context of the following judg- 
ments, and how far does it enter into their internal organisations : 
In the spring a young man's fancy lightly turns to thoughts of love. 
Beans and cucumbers nearly always die of some blight. Life is not 
what it used to be? 

3. Wlhat is the wider intellectual context of 'the following judg- 
ments, and how far does it enter into their internal organisation : 
Water is H2O. Marius conquered the Cimbri and Teutones. Some 
day the air-plane will supersede the automobile? 

4. What is the wider intellectual context of the following judg- 
ments, and how far does it enter into their internal organisation : 
Things in themselves are unknowable. I have taken all knowledge to 
be my province — I shall be omniscient. The Future Life will be the 
present life over again, but raised to the nth power? 



CHAPTER IX 
THE INTELLECTUAL ELEMENT AND VALIDITY. 

The Question of Validity. — So far we have seen that the 
function of intellect in judging is to split up the material 
of sensory consciousness, to take it apart into its elements, 
and then re-shape it nearer to the desire for relevance, con- 
sistency, systematic unity. This is done by introducing the 
standards of identity-in-difference, difference-in-identity, and 
organisation, both internal and external, until at last the 
material of the sensory consciousness has been so worked 
over that it is able to take its place in a single organised 
system, in which every element is rational, relevant, coherent 
with every other element, and the whole structure down to 
its minutest details is consistent, thinkable through and 
through, and organic with a meaning which constitutes one 
great identity-in-difference, a single system, an ideal indi- 
vidual. 

All this, however, is merely descriptive. It tells us how 
the intellect functions, what it does. But there is a further 
question, the question of validity. Granted that the intellect 
functions in this kind of way, is what it does legitimate? 
Can we justify the great changes brought about by intel- 
lectual organisation? By what right do we analyse and 
reconstruct? That our meddling intellect mis-shapes the 
beauteous forms of things, mutilates reality and imprisons 
it within a net-work of man-made frames, conceptual abstrac- 
tions in which is neither life nor truth — in this view poet 
and philosopher are frequently at one, and never more so 
than at the present day. That the work of "discursive" 
thought is thus infected with falsity, is a conclusion not 
lightly to be set aside. The question must therefore be faced 
— How far is the work of intellect valid? 

Here, for the sake of clearness, we must introduce a 
distinction between a more general, and a more special ques- 
tion. What our poets and philosophers mean, when they 
suspect the intellect of misleading us, is that truth resides 

92 



THE QUESTION OF VALIDITY 93 

in intuition, sensation, sympathy, immediate awareness, 
whereas intellect gives us an awareness which is mediate, 
not the thing itself, but a conceptual model, a structure which 
we can substitute for the reality. We can understand this, 
because we have ourselves constructed it. It works as well 
as if it were the original, but — it is not the original. This 
objection to the work of intellect opens up a more general 
question than we are at present in a position to discuss. It 
compares and balances the respective value-claims of intellect 
and intuition, or intellect and sensation, and thus presupposes 
an answer to two more special questions, (1) concerning the 
validity of intuition or sensation, and (2) concerning the 
validity of intellect. So far, we have only answered the 
first of these more special questions. We have treated of 
the sensory element, in abstraction from the intellectual 
element. It remains, therefore, to attack the second of these 
special questions. We must leave on one side the question 
of sensation and sensory validity, and examine how far, if 
at all, the intellect, qua intellect, is valid, i. e., the question 
of intellectual validity. After this question is answered, if 
we succeed in discovering the work of intellect to be intel- 
lectually valid, we can then proceed to the general question, 
and ask how far the working of a mind which is intellectually 
sans peur et sans reproche compares with sensory validity, 
as a factor in attaining reliable knowledge of reality. 

Let us take an example. If the truth of a scientific hypoth- 
esis is called in question, we can, as we say, verify it by 
an appeal to sensory experience. This is true, and has been 
already considered. But there is a prior question, viz., how 
far the hypothesis is intellectually satisfactory, how far the 
intellectual structure, the conceptual model, is really intel- 
ligible, whether it really hangs together and is rational and 
meaningful. It is the conditions of this meaningfulness which 
we must now examine. Let us take a concrete instance from 
the field of simultaneous equations. "If three hens lay on 
the average as many eggs as four ducks, and the number 
of eggs laid in a month by six hens and six ducks is a hundred 
and eighty, what is the weekly average of each hen and each 
duck?" The intellectual element in the solution consists 
in the introduction of sharply differentiated identities such 
as x and y, in such a form that the conditions of the problem 



94 INTELLECTUAL ELEMENT AND VALIDITY 

are expressed somewhat thus: "3x=4y, and 6#+6i/=180X7." 



30 
The further manipulations of these conventionalised identi- 
ties according to the rules of algebra or geometry inform us 
with mathematical certainty, that the weekly average of each 
hen is four eggs, and of each duck three eggs. Here, then, 
are judgments which are intellectually valid. On what does 
their intellectual validity depend? 

It depends (1) on the introduction of identity-in-difference. 
If x did not have a core of identity in the various propositions, 
in spite of its varying fringe of relations, if, for instance, it 
meant in the second equation something entirely different 
from what it meant in the first, no result could be reached. 
It depends (2) on the introduction of difference-in-identity ; 
for if x and y did not have some variations, some differences 
of. meaning in their varying contexts, then, as we have seen, 
no movement of thought could take place; nothing would be 
judged. It depends (3) on the organisation of these identi- 
ties and differences with reference to one another in a single 
act of thought; for instance, if the first and second equations 
were not somewhere brought together, no conclusion could 
be reached. Finally it depends (4) on the external organi- 
sation of these conventionalised elements within the wider 
system of algebra or geometry, with all which this implies. 
The result is reached by adhering strictly to the rules of 
algebra or geometry, i. e., to the rules of mathematics, which 
is a kind of applied logic and belongs to the system of what- 
ever can be thought. If we sum up what we have seen, we 
can state that intellectual validity in the case before us 
consists in observing strictly the rules upon which organi- 
sation of intellectualised elements within a single consistent 
system depends. So far as the analysis and subsequent recon- 
struction are governed strictly by reference to the ideal of 
this single system, the result is intellectually satisfactory. 
So far, however, as any of these rules are not observed — e. g., 
if the elements are not identities, or are not to some extent 
different, or are not organised internally or externally — so 
far no result can be reached with which we can be intellectu- 
ally satisfied. 

Let us now proceed to ask how far, in our various typical 



IX JUDGMENTS OF PERCEPTION 95 

forms of judgment, the intellectual structure admits of intel- 
lectual validity. 

In Judgments of Perception. — Take such a judgment as 
"This room is warm." As we have already seen, sensation 
alone assures us primarily of a feeling of warmth. The judg- 
ment, however, that the room is warm, adds something 
further, an element of interpretation, which we have regarded 
as intellectual. This element consists, as we have seen, of 
an analysis of the sensory consciousness into certain ele- 
mentary experiences which are then reconstructed, not merely 
in reference to present sensation, but also in the light of a 
wider system of knowledge, partly experiental and partly 
symbolic, partly practical and partly reaching out into physics 
and logic with all which these imply — i. e., ultimately the 
elementary experiences are reconstructed in terms of the 
single system of organised knowledge, of what can consist- 
ently be thought. It is this reference to the wider structure 
which enables us to pass beyond the present sensation and 
state, not merely that ice feel warm, but that the room is 
warm, and the furnace probably requires attention, or there 
may be danger of a fire, etc. The intellectual element, then, 
consists in realising, in making concrete, the lines of intel- 
lectual continuity which give our perceptual judgment its 
place in the system of thinkables. 

On what does the validity of this procedure — if it is valid — 
depend? Let us consider the steps we have taken, in order. 
The first step consists, as we have seen, of analysing our 
sensory experience into elements which are conventionalised, 
taken out of their sensory contexts and made discontinuous, 
cut off and fixed by the mind so as to retain a certain identity 
of meaning, however various the intellectual contexts into 
which they may subsequently be thrown. These mental 
counters, then, which are thus utilised as bricks in building 
up the intellectual structure, are what we have called "identi- 
ties-in-difference." Those used in constructing the logical 
subject of discourse — the room — are predominantly spatial 
experiences, and those from which we construct the logical 
predicate — warm — are predominantly temperature-values. If 
these elements were not conventionalised, if one identical 
meaning did not underlie them and keep them substantially 
the same in different contexts, if they remained vague and 
fluctuating in meaning, — then farewell to consistency and 



96 INTELLECTUAL ELEMENT AND VALIDITY 

unity, i. e., to intellectual validity. For what is inconsistent 
is invalid, and what does not form a unity is a multiplicity 
without coherence or consistency. As far, then, as these 
elementary experiences are strictly fixed by the mind and 
used as "identities-in-difference," i. e., as retaining the self- 
same core of meaning, whatever the intellectual context into 
which they may enter, — so far we have a basis upon which a 
consistent and intellectually valid thought-structure may be 
erected. Conformity to the standard of identity-in-difference, 
then, is a condition sine qua non of intellectual validity 

A second step in the intellectual procedure is the introduc- 
tion of the standard of difference-in-identity, i. e., of different 
fringes of meaning according as our "identities" enter dif- 
ferent contexts. We have already seen that apart from such 
difference, no movement of thought, and thus no judgment, 
could take place. The introduction of difference-in-identity — 
a fringe of difference which does not annul the underlying 
identity — is thus a second necessary condition sine qua non 
of intellectual validity. 

The third step is organisation, internal and external. If 
the elementary experiences are not brought together and 
unified, i. e., organised so as to give us the complex structures 
8 and P, then there is no subject of discourse and no logical 
predicate, which means that nothing is judged about anything, 
i. e., no judgment takes place. Further, if 8 and P are not 
brought together, if "the room" and "warm" are not held 
together in a single act of thought which unifies them without 
annulling their differences, no judgment takes place. For 
judging is essentially a function of unity, and we certainly 
unify the 8 and P concepts in judging that 8 is P, the room is 
warm. In other words, internal organisation is a conditio 
sine qua non, a, necessary condition of judgment. Further, 
if the lines of organisation which have thus given us the 
internal structure of the judgment are not intellectually con- 
tinuous with a wider intellectual structure — if the judgment 
is not continuous in meaning with temperature-judgments, 
practical judgments, and ultimately with the whole organi- 
sation of rational experience — then it is inconsistent and 
irrational, i. e. f intellectually unsatisfactory. Thus we see 
that it is only so far as our perceptual judgment is intellectu- 
ally continuous with the system of thinkables — i. e., only so 



IN JUDGMENTS OF EXPERIENCE 97 

far as it is relevant, consistent, and rational through and 
through, that it can be regarded as intellectually satisfactory. 

In Judgments of Experience. — Take such a judgment as 
"The freight-trains crossing the bridge are growing more 
troublesome every year." As we have seen, the process by 
which the senory consciousness is here raised to the intel- 
lectual level, consists in splitting up the spatial and temporal 
continuum and selecting elementary experiences of train- 
disturbances, taking them from their sensory context and 
transforming them into mental counters, identities-in-differ- 
ence which are then utilised in the further construction which 
builds up 8 and P and gives us the organisation which is our 
judgment — a structure not merely internally organised, but 
in its main lines intellectually continuous with the wider 
structure of practical judgments, and ultimately of all which 
can rationally and consistently be thought in a single system 
of meaning. Our question is, on what does the validity of 
this intellectualising process — if it is valid — depend? For 
instance, take the first step. Would the procedure be intel- 
lectually satisfactory if our analysis did not result in giving 
us conventionalised elements, identities-in-difference? Let 
us see. If there is no identical reference-point governing the 
selection of elements out of which 8 and P are to be con- 
structed, then the ^-concept will be composed of all kinds of 
heterogeneous elements without real unity — a mixture of 
vague, fluctuating experiences not all strictly relevant to the 
concept "train disturbances." Such unintelligent groupings 
would certainly not be clear enough or sufficiently to the 
point to be used as an intellectual subject of discourse, and, 
in fact, as we have seen in perceptual judgments, the strict 
introduction of identity-in-difference would seem to be a sine 
qua non of intellectually valid thinking. What is true of the 
elementary experiences which are grouped together in order 
to form 8 and P is, of course, true also of £ and P themselves 
and indeed of the general meaning of the judgment. Each of 
these must have its own clearly apprehended meaning, an 
identical direction of thought underlying any change of intel- 
lectual context, if the resultant structure is to be intellectually 
satisfactory. 

In the second place, the introduction of difference-in-identity, 
as we have already seen, is similarly a sine qua non of valid 
thinking, indeed of thinking at all. Without some difference 



98 INTELLECTUAL ELEMENT AND VALIDITY 

resulting from the varying fringe of relations contributed by 
the contexts into which 8 and P, for instance, enter, no move- 
ment of thought could take place, nothing would be judged. 
In the third place, organisation of the various elementary 
train-disturbance experiences so as to form 8 and P, and of 
8 and P themselves within the single act of thought which 
is the judgment, is necessary; and finally, if the general lines 
of internal organisation are not strictly continuous with the 
general lines on which the whole system of thinkable, con- 
sistent, and rational judgments is constructed, then the result 
fails to cohere, and is thus intellectually unsatisfactory. In 
this way we realise that intellectual validity in the case of 
experiential judgments depends on strict conformity to the 
intellectual standards of identity, difference, and organisation. 
It is only so far as the analysis results in identities with 
fringes of difference, organised so as to form an integral por- 
tion of the vast system which includes all which can be con- 
sistently and rationally thought, that the judgment of experi- 
ence can be regarded as intellectually satisfactory. 

In Symbolic Judgments. — Symbolic judgments have already 
been dealt with, at least in principle, in the simultaneous 
equation case considered above. What makes this a case 
of the "symbolic" type of judgment is not so much the fact 
that algebraic symbols were employed in its solution, as that 
it reconstructs for us, by indirect methods, a summing up 
of experiences which goes beyond what we have actually 
experienced. The statement of the average number of eggs 
to be expected per hen, for instance, is more than a mere 
summing up of past experiences; it gives us a rule which 
holds e. g., for future experiences, for experiences which have 
not been, and indeed may never be ours, in a word, the judg- 
ment moves in the field of possible human experience. It 
thus belongs to the sphere of what we have called "symbolic" 
judgments, and we may take what we saw there and apply 
it briefly to our typical instance of a symbolic judgment, 
"Rome was occupied by Caesar." The steps by which, in 
this typical case, the sensory consciousness becomes raised 
to the intellectual level consist (1) in the analysis which 
results in mental counters composed of blue-sky experiences, 
panic and triumph experience, etc., taken out of their original 
sensory contexts and fixed by the mind in the form of identi- 
ties-in-difference, (2) in the introduction of difference, i. e., 



IN TRANSCENDENT JUDGMENTS 99 

different shades of meaning according to variations of intel- 
lectual context — into the "identities" — and (3) the organi- 
sation, both internal and external of these differentiated iden- 
tities, which results in giving us a judgment which does not 
stand by itself, but is part and parcel of whatever is rational 
and meaningful, and helps to constitute the single system of 
whatever can consistently be thought. It is unnecessary to 
inquire in detail concerning the intellectual validity of this 
judgment. Briefly and in principle, it is only so far as these 
intellectual standards of identity, difference, and organisa- 
tion are followed, only so far as the resulting structure really 
does constitute an integral portion of the system of think- 
ables, only so far as it is intellectually continuous with all 
which is rational, consistent, and coherent, that it can be 
regarded as intellectually satisfactory. 

In Transcendent Judgments. — Transcendent judgments are, 
as we have seen, a kind of extended symbolic judgment, so 
that the conclusions as to intellectual validity which we have 
found to hold good in the case of symbolic judgments can be 
transferred, without alteration in principle, to transcendent 
judgments also. And in fact, if we examine the thought of 
our professed metaphysicians, we find without much difficulty 
that it is on the standards already studied that they rely for 
the intellectual validity of their constructions. The attempt 
to construct the outlines of the Absolute Experience is almost 
always guided by considerations of systematic consistency, and 
the ideal of rational thinkability is openly acknowledged as the 
highest standard to which one can appeal. We shall there- 
fore conclude without further examination, that in such judg- 
ments as "God is a substance with infinite attributes," "Things- 
in-themselves are unknowable." "The real is the rational," and 
so forth, the intellectual validity of such constructions depends 
upon strict conformity to the standards of identity, difference, 
and organisation, and that it is only so far as such judgments 
are strictly consistent and cohere in a single, all-inclusive uni- 
verse of rational meaning, that they are regarded as intel- 
lectually satisfactory.! 

Conclusion — Intellectual Validity. — If we now put together 
what we have discovered in our discussion hitherto, we realise, 
that while all judgments have a sensory, as well as an intel- 

1 Cf . e. c/., F. H. Bradley. Appearance and Reality, latest edition. 
Appendix I ; Bosanquet, Logi-c Vol. I, pp. 3-8. 



100 INTELLECTUAL ELEMENT AND VALIDITY 

lectual aspect, it is only so far as they conform to intellectual 
standards that they can claim intellectual validity. It is only 
so far as intellectually irrelevant elements — such as we find 
vaguely embodied in the continuous stream of sensory con- 
sciousness — are removed, and we have strict organisation of 
strictly intellectualised identities within a single system which 
includes in principle all that can consistently be thought — 
that the resulting structure can be regarded as intellectually 
satisfactory. A judgment, then, is intellectually valid, precisely 
in so far as it is fitted, without further qualification or trans- 
formation of meaning, to enter into a system of relations which 
includes every thought which is rationally consistent, and thus 
itself intellectually satisfactory, the kingdom of Truth.2 

2 Cf . Kant, Critique of Pure Reason (tr. Meiklejohn), pp. 26-27. 
The view taken in the text is approximately the same as Kant's when 
he says that only that which reason constructs according to rational 
principles is entirely intelligible and satisfactory. 

FOR FURTHER READING 

F. H. Bradley, Principles of Logic, Bk. I, chapter i. B. Erdmann, 
Logik, (2nd Edit.), pp. 194-197, 409-426. 



EXERCISES 

1. On what does the intellectual validity of the following judg- 
ments depend : You are looking sun-burned. This leaf is turning red. 
This new varnish feels sticky? 

2. On what does the intellectual validity of <rhe following judg- 
ments depend : We usually put on the storm windows towards the 
end of October. Our tomato-es ripen well indoors, if we allow the 
sun to get to them. The neighbor's baby nearly always cries at night ? 

3. On what does the intellectual validity of the following judg- 
ments depend : None but the brave deserve the fair. Demosthenes 
was a great orator, but a poor statesman. 5340 — 2189 = 3151 ? 

4. On what does the intellectual validity of the following judg- 
ments depend : All genuine knowledge is independent of experience. 
We shall be as God, knowing both good and evil. As it was in the 
beginning, is now, and ever shall be, world without end. 



CHAPTER X 
THE VALIDITY OF JUDGMENT 

The Problem. — So far we have discovered by analysis of our 
thought two aspects of every judgment, (1) the sensory, and 
(2) the intellectual. We have further seen that each of these 
aspects has its own laws, and that it is only by strictly con- 
forming to these laws that each aspect possesses validity 
within its own sphere. So far as our thought is sensory, it 
is valid provided that it is a continuous sensory expansion from 
the focus of sensory consciousness, — continuous, that is to say, 
in space and time. So far as it is intellectual, our thought is 
valid so far as it constitutes an integral portion of that 
organised totality which ideally contains all which can con- 
sistently he thought and can rationally cohere in a single 
system of meaning. Sensory continuity is one thing; intel- 
lectual consistency is another; and we have already seen that 
these are not perfectly proportioned to one another in our 
concrete thinking. In perceptual judgments, the sensory ele- 
ments almost everything; but as we advance towards sym- 
bolic and transcendent judgments we notice more and more 
the gulf between what sensation can give and what the ideal- 
ising intellect demands. The sensory element can be spread 
out, so to speak, so as to cover the field, not merely of actual, 
but also of possible human experience. But as we gradually 
approach the place where the symbolic begins to pass into the 
transcendent type of thinking, the sensory covering has become 
so thin that at last it is totally inadequate to satisfy the needs 
of intellect. Sense and intellect are thus, to some extent at 
least, heterogeneous, and sense covers a less wide field than 
intellect. What is their inter-relation, and which of them plays 
the major part in contributing, not to the specifically sensory, 
or specifically intellectual validity of judgment, but to the gen- 
eral validity of our thinking? This is our present problem. 

Idealism. — Many thinkers, from Plato down, l^ave assigned 
the palm to intellect. For such thinkers, "the sensory," or 
the content of the sensory consciousness, is not an object of 

101 



102 THE VALIDITY OF JUDGMENT 

strict knowledge. It is too vague, and fluid, and refuses to 
lend itself to the manipulations of accurate and systematic 
thought. It is only so far as we conform strictly to intellectual 
standards, and leave behind us the sensory element, that we 
attain to truth, or knowledge of real Being, a knowledge which 
extends infinitely beyond what our limited senses can hope to 
realise. For Descartes and Leibniz, for instance, in modern 
philosophy, sense is simply confused thinking, thinking con- 
fused by connection with our bodily sense-organs, and it is 
only so far as the mind separates itself from these disturbing 
influences and thinks by itself, that it can attain to clear and 
distinct apprehension of its object. So too in our own day it 
is not difficult for a writer like Bradley to show that the chief 
viewpoints of empirical science fail to conform strictly to 
intellectual standards, and thus present us with a kind of 
knowledge which deals only with phenomena, not with Reality 
— i. e., not with the kind of object which would fulfill the ulti- 
mate aspirations of pure intellect. The great Idealists have 
thus almost all disparaged sensation and exalted intellect, to 
such an extent that, as notably in the systems of Plato and 
Hegel, intellect tends to occupy the entire field, and the field 
of knowledge is taken to coincide with the field of transcendent 
thought. 

Sensualism. — A different group of thinkers, of whom per- 
haps Condillac is the chief representative, regard the sensory 
element as of predominant importance. For such thinkers, to 
judge is to perceive a relation between two ideas. The per- 
ception of such a relation is a matter of comparison, and com- 
parison is a matter of attending to two sensations. Judg- 
ment thus means attending to two sensations. But attention 
itself is not an intellectual act. Attention means, having our 
capacity for feeling wholly taken up by the impressions made 
upon our sense-organs, and these impressions are modifica- 
tions of our conscious selves, i. e., of our sensibility. Thus we 
see that judgment is a matter of having our capacity for feel- 
ing wholly taken up by two impressions, or, more simply, hav- 
ing our sensibility modified in two ways, i. e., having two sen- 
sations. Attention is thus not a specifically "intellectual" 
operation. Jt is simply a question of being conscious of sen- 
sations, and such thinkers tend to regard all the more elabo- 
rate structures of science and philosophy as valid only so far 



SOLUTION OF THE PROBLEM 103 

as they can be reduced, without remainder, to simple sensa- 
tions.i 

Solution of the Problem. — Both these views are one-sided. 
It cannot be too strongly insisted upon, that sensation with- 
out intellectual organisation is blind, and intellect without 
sensory content is empty. Everything which we regard as 
meaningful, rational, clear-cut, and intelligible is to some 
extent the result- of intellectual operation. A "pure" sensa- 
tion, i. e., a sensation purified of every intellectual element, 
would be without organisation, without identity or fixity, a 
fleeting psychical entity which we could never quite grasp and 
apprehend. In fact, seizing, grasping, and fixing is essentially 
the work of intellect, an intellectual operation necessary to 
understand anything, introducing, as it does, order, system, 
rationality, meaning into what would otherwise be incoherent 
and chaotic. It picks out from the sensory consciousness 
everything which is relevant, and lets the rest go. It tele- 
scopes the sensation, so to speak, and makes the meaningful 
elements stand out in sharp relief. In other words, the intel- 
lectual concept is the sensation, but only so far as the sensa- 
tion contained elements of meaning. It is the essence, the 
meaning, the concentrated extract, as it were, of the sensory 
consciousness. Just as a bottle of beef-extract is supposed to 
represent the concentrated food-value of the ox, so does the 
intellectual concept represent the concentrated meaning-value 
of the sensory consciousness. Scientific method is simply an 
efficient intellectual machine, into which one puts the vague 
and confused mass of feelings, sensations, etc., in order to grind 
out clear-cut elements which can be used for constructing 
science. 

On the other hand, without sensory content intellect can 
accomplish nothing. One cannot make bricks without straw; 
and the application of scientific method cannot, however 
methodic the scientist may be, extract from the data more 
than is there to be extracted. No amount of scientific manip- 
ulation of mathematical or physical material, for instance, can 
produce valuable decisions on ethical or religious questions, 

i Etienne Bonnot de Condillac, Traite des Sensations, Paris and 
London, 1754. See Rand, Modem Classical Philosophers, pp. 347-375. 
This way of thinking is usually attributed to the British school of 
thought which commences with Locke. Cf. Locke's Essay (1690- 
1700), Bk. II. Cf. also J. S. Mill, Examination of Sir William Hamil- 
ton's Philosophy, chapter xi (Rand, pp. 690-702). 



104 THE VALIDITY OF JUDGMENT 

just as no amount of card-indexing our ethical or religious 
convictions can tell us anything about the validity of biological 
theories of evolution. We need, it is true, all the applied 
logic, all the scientific method, of which we are capable. But 
we must recognise, and never allow ourselves to forget, that 
logical acumen alone will never lead to valuable results. It is 
necessary also to have material with which to work, and this 
material comes from the sensory consciousness. Both intel- 
lect and sensation are necessary, if we are to attain to results 
of general validity. 

Let us take an example. Any one who has had to solve 
many problems by means of simultaneous equations, for 
instance, knows well how easy it is to make some slight error 
in the preliminary analysis which results in the two x and y 
equations. The conventionalised expression often fails to rep- 
resent strictly the concentrated extract of the popular expres- 
sions of general language. In such cases, the subsequent oper- 
ations with # and y may take place with consummate skill, 
but if anything vital has been omitted or added, the final 
result, however valid intellectually, fails of attaining general 
validity. The answer, as we say, is wrong, though some mark 
may be given for the working. There has been a mistake in 
fact, and it is only by patient reference to the material, by 
repeated sense-experiences, that we can hope to rectify such 
mistakes.2 

Application. — Let us apply this solution briefly to our typi- 
cal instances. (1) The validity of "The room is warm" will 
depend wholly upon whether this judgment is a correct inter- 
pretation of the sensory consciousness, the feeling of warmth 
which I undoubtedly experience. My judgment consists in an 
organisation of this consciousness, the application of scientific 
method with all its standards, in order to extract from it the 
essence or meaning-value which it contains. The validity of 
the result depends, in the first place, upon whether the analysis 
and reconstruction is itself intellectually valid, i. e., whether 
it is consistent and rational — this is a sine qua non — but also, 
in the second place, whether the result harmonises with the 
sensory starting-point. If I conclude that the temperature of 
the room is normal, while my sensations continue to assure 
me that I feel warm, then something is wrong. The hypothe- 

2 Cf. Erdmann, Logik, pp. 372-413, esp. p. 374. 



APPLICATION OF SOLUTION 105 

sis of the room's being warm must be succeeded by a question 
as to whether I myself am in some pathological, feverish state, 
etc. That is to say, as in the simultaneous equation above, 
there may have been some mistake about the preliminary 
analysis, the pathological symptoms having been overlooked. 
In other words, in order to verify a perceptual judgment it is 
necessary (1) to be sure that the result is intellectually satis- 
factory, and (2) to be certain that it really does represent the 
meaning, the concentrated essence, of the sensory conscious- 
ness which it professes to interpret, and this can only be 
assured by patient reference to the sensory, as well as to the 
intellectual side of the experience. 

(2) So too in the experiential example. In such a judg- 
ment as "The freight-trains crossing the bridge are growing 
more troublesome in recent years," error, or lack of validity, 
is almost always a matter of lack of thoroughness in the intel- 
lectual analysis. The disturbance is annoying, and without 
really making a clear-cut, exact, scientific comparison with 
previous experiences, we allow ourselves to jump — without 
thinking — to the conclusion that it is more troublesome than 
it used to be. Or it may be merely that we are personally 
growing more sensitive. It will be important, in dealing later 
with the railway company, to know precisely which of these 
is the case. The verification of our conclusion, therefore, will 
involve both the application of strict scientific method and 
patient reference to the sensory consciousness which extends 
back from the present to the past cases of similar disturb- 
ances. The judgment of experience will thus be valid so far 
as it is a correct interpretation of the experiences in ques- 
tion, i. e., (1) correctly put together in accordance with intel- 
lectual standards, and (2) correctly applied to the particular 
experiences of disturbing freight-trains. 

(3) The case of symbolic judgments has already been con- 
sidered in principle in dealing with the simultaneous equation 
example above. It remains to apply our results briefly to the 
judgment of Rome being occupied by Caesar. The validity of 
our conclusion depends on the correctness with which we have 
interpreted the printed text of our history book, which in turn 
goes back to the interpretation of various classical manuscripts 
and archeological evidences. It is well known that momen- 
tous conclusions in history have at times been based upon very 
slender evidence. The ideal of reaching valid conclusions in 



106 VALIDITY OF JUDGMENT 

this field, then, demands not only the strictest use of clear 
thinking, but also the most careful study of the data before 
the student — i. e., the visual sensations, or sensory conscious- 
ness of the reader. Only thus can we be sure that the inter- 
pretative structure is really based upon experiential, sensory 
foundations. Both intellectual and sensory validity are nec- 
essary to secure the general validity of the symbolic judgment. 

(4) Transcendent judgments, in the nature of the case, are 
incapable of direct sensory verification. All that we can do is 
(1) to test our thinking concerning "things-in-themselves," or 
whatever our transcendent entities may be, by reference to 
intellectual standards, and then (2) to connect it with what- 
ever sensory experience we may have which bears upon the 
question. These ultimate conclusions of speculative thought, 
these metaphysical edifices, are all supposed to represent the 
final truth of our experience, to give the concentrated essence 
or meaning-value of experience as a whole. But this includes 
our actual experiences here and now, so that the intellectual 
acumen of the philosopher represents only one side of the 
question. His results must really apply somewhere to our 
empirical experiences also, if they are to be regarded as of 
general validity. Not only intellectual, but sensory validity 
also is, then, necessary in the case of transcendent judgments. 

Conclusion — Theory of Judgment.— Let us now try to put 
together the whole of our preceding discussions, let us prac- 
tise what we have just been preaching, and endeavor to extract 
the kernel of meaning from the material which has sur- 
rounded it in varying ways from the first page to the present. 
Our conclusion is, that judgment is the intellectual organisa- 
tion of sensory experience, the introduction of intellectual 
standards into the sensory consciousness so as to give us, in 
place of the even but vague sensory flow, a clear-cut intel- 
lectualised essence which is fit to take its place in the ultimate 
ideal of organisation, the system of knowables. This system 
is not only thinkable through and through, but must be con- 
nected with the sensory consciousness in such a way that our 
judgments can be verified, can be, not merely thought, but 
known. The conceptual, intellectualised essence must be the 
essence of the sensory experience, i. e., must give us a mean- 
ing which is not a pure creation of intellectual manipulation, 
but is implicitly present from the very first, embedded in our 
experience even at the sensory level. Judgment, then, is both 



THEORY OF JUDGMENT 107 

sensory and intellectual; it is the intellectual organisation of 
sensory experience, and is valid precisely so far as it is what 
it professes to be. If the sensory side of the experience is 
acceptable to direct sensory apprehension, and the intellectual 
organisation is thoroughly consistent, and if, finally, the judg- 
ment is the intellectual organisation of the sensory experience 
in question, then the judgment is valid. 

FOR FURTHER READING 

B. Bosanquet, Dogic, Vol. I, pp. 72-92. F. H. Bradley, Principles 
of Logic, Bk. I, chapter i. H. Lotze, Logic, pp. 140-148. 

EXERCISES 

1. On what does the validity of the following judgments depend: 
These gloves are very comfortable. This water is too hot to drink. 
This grain elevator is larger than that? 

2. On what does the validity of the following judgments depend : 
We nearly always go to church on Sunday. As a general rule, the 
children seem — so far as I have seen — to prefer the slide to the 
swings. We seem to wake up to life again when the spring comes? 

3. On what does the validity of the following judgments depend : 
Conscience is but a word which cowards use, devised at first to keep 
the strong in awe. Shakespeare borrowed nearly all his plots from 
other writers. Blue litmus paper turns red, when dipped into acid? 

4. On what does the validity of the following judgments depend : 
The termination of this life is the beginning of a new existence. The 
aim of my life is mystical absorption in Divinity. The vision of 
absolute beauty raises us above the human level? 



APPENDIX TO PART I 

NEGATION 

The Problem. — Traditional logic, from the time of Aris- 
totle to the present day, has recognised a distinction of judg-' 
ments as affirmative and negative. "S is P" is an affirmative 
judgment, and "8 is not P" is a negative judgment. For tra- 
ditional logic this distinction is of major importance. Modern 
logic, on the other hand, regards the distinction as of minor 
importance. Lotze treats judgment as the answer to a ques- 
tion "Is S r P?" (i. e., Does S stand in a certain relation to 
P?), and observes that whether we answer Yes or No makes 
no difference to r, i. e., to the logical character of the relation. 
Whether affirmed or denied, it remains the relation 8 r P, and 
a distinction where there is no difference of relation is of 
little importance for logic. Wundt and Erdmann somewhat 
similarly regard the distinction as of secondary importance, 
and we have accordingly not dealt with it in the text. But 
unless properly understood, negation gives rise to so many 
difficulties of interpretation, that it is necessary to deal with 
them in an appendix. The two chief difficulties are, (1) that 
negation is subjective, and (2) that negation is indefinite. 

Is Negation Subjective? — Let us take a few instances. 
Things-in-themselves are not knowable. Virtue is not square 
or hexagonal. No men-who-are-not-brave deserve the fair. 47 
plus 89 do not make 130. All is not gold that glistens. Stone 
walls do not a prison make, nor iron bars a cage. There is 
no such thing as "apperception." I am not in love. This color 
is not brown. . . . These examples cover the whole field 
of judgment, and with such instances in view we can ask, Does 
negation give us any information which could be called posi- 
tive? Does it add to our knowledge of reality? Has it, in a 
word, objective value, or is it merely subjective? 

Let us consider. "Things-in-themselves are not knowable." 
Does this tell us anything about "the knowable, ,, or about 
"things-in-themselves ?" Does it even assert indubitably that 
there are such entities as things-in-themselves or knowledge? 

108 



NEGATION 109 

For modern logic, on the whole, the answer to each of these 
questions is No. "Virtue is not square" seems to note a posi- 
tive failure on our part to connect ethical and mathematical 
values, perhaps comparable to the failure to get to know any- 
thing about things-in-themselves. To know that "no cowards 
deserve the fair" does not tell us that any one does deserve 
the fair. Perhaps merit does not enter into the case at all. 
To know that "47 plus 89 do not make 130" does not tell us 
what they do make. From such considerations, a tendency has 
arisen to regard negation as registering a failure of some ideal 
experiment of ours. We have constructed, in the unsubstantial 
region of the imagination, a relation S r P and proceed to 
interrogate reality, to see whether it will accept our hypothe- 
sis. If we can verify it, if reality accepts our ideal sugges- 
tion, well and good; we have added to the sum of knowledge. 
But if reality refuses to accept our hypothesis, we must try 
again. The only positive conclusion is that we have failed. 
We cannot even be certain that reality is otherwise than we 
have supposed. It may be merely that we have failed to con- 
nect our supposal properly. Many a correct hypothesis in 
science has been abandoned for a time because in the then 
state of knowledge it could not be verified. In such cases it is 
not possible to say of such a relation S r P either that it is, 
or that it is not. All that can be stated correctly is that 
we do not know whether or no. We do not know whether 
things-in-themselves are absolutely unknowable, whether ethics 
and mathematics are hopelessly disparate departments of expe- 
rience, whether the fair can or can not be deserved by any 
combination of manly qualities. All that we do know is that 
we have failed hitherto to discover a satisfactory answer. In 
other words, the value of negation is subjective rather than 
objective. It throws us back upon ourselves, and ends in the 
Socratic recognition of ignorance. 

Is this all that we can say? Is the search after knowledge, 
as the psychologists tell us, a matter of trial and error, hit 
or miss? Are we to say the whole value of the negative judg- 
ment consists in registering a miss, in realising that we are 
somehow in error and must try again? Even if so, we can- 
not stop with this statement. For to know that we are in 
error is to know something positive, to add to some extent to 
the sum of human knowledge. It may not tell us much about 
epistemology or ethics or mathematics, but it does tell us 



110 APPENDIX 

something about ourselves. But since we are also elements 
within the real world, the Socratic conviction of our own 
ignorance will have some objective significance. To know that 
we have failed, that we cannot, at least at present, verify our 
hypothesis, involves some positive knowledge about the uni- 
verse of discourse within which our ideal experiment is 
applied. Reality-as-we-conceive-it rejects our hypothesis. 
Good. We must, then, have some conception about reality, and 
our failure amounts to this, that we recognise an incompati- 
bility between two of our conceptions about reality. One is 
accepted as — at least in part — verified. The other is rejected, 
at least as being inconsistent with the first. It is possible that 
the first is not entirely inconsistent with the second; it may 
be merely that we cannot, are not in a position to realise the 
deeper viewpoint which will ultimately reveal an underlying 
unity and consistency. We thus recognise an inconsistency 
within the realm of knowledge, and it is this recognition of 
inconsistency which convinces us of failure and throws us 
back upon ourselves. The negative judgment is thus at least 
the positive recognition of inconsistency, otherness or differ- 
ence in the world of knowledge. We can, if we wish, define 
this as "subjective. " But if we can recognise differences 
within one sphere of knowledge, why not also in another, 
(say) in physics or mathematics? 

Let us consider further. So far we have been proceeding 
upon a somewhat one-sided view. We have been assuming 
that the suggested relation r is affirmative in character. Let 
us now take the other alternative. Let us suppose the rela- 
tion to be negative, a suggestion that perhaps 8 and P are 
objectively different. We form the ideal hypothesis that a 
square is not a circle, that virtue is not three-cornered, that 
cowardice, at any rate, does not merit feminine favor. We 
proceed to interrogate reality, and find that it accepts our 
idea. Well and good. The hypothesis is verified, and the sum 
of objective knowledge is increased. We have established a 
fact, the fact of some objective difference, and can no longer 
maintain our Socratic pose of ignorance. We know, and we 
know by means of a negative judgment. The negative judg- 
ment can thus serve to give us objective knowledge. 

It is thus misleading to regard the affirmative judgment as 
monopolising objective knowledge, and to treat the negative 
judgment as exclusively subjective. The truth seems rather 



NEGATION 111 

to be that both forms alike possess not only a subjective, but 
also an objective reference. If then in affirmation we are in 
undeniable contact with reality, the same statement holds 
good of negation also. In both cases we are apprehending an 
objective relation, a relation which really obtains between ele- 
ments of reality. The difference between affirmation and nega- 
tion is not the difference between establishing and failing to 
establish contact with reality. Contact is established in both 
cases. The difference is only in the kind of relation appre- 
hended. There are, on the one hand, relations of inclusion or 
identity, and on the other, relations of exclusion or differ- 
ence; and both kinds of relation are equally objective. "An 
electric bulb is not a typewriter." This deals with a perfectly 
objective relation. An electric light is other than, different 
from, a typewriter. You cannot substitute the one for the 
other. Recognition of such differences and distinctions in the 
objective world is often even more essential to our safety than 
recognition of identities. "That ladder is not safe," "The ice 
is not strong enough," "The paint is not dry," "The train does 
not stop here, unless you ask the conductor," "X is not to be 
trusted in money matters." If we were unable to rise above 
the subjective stage of asking questions and failing to answer 
them, if we failed to establish contact with reality in such 
practical, every-day negations, who can doubt that our life, as 
Hobbes puts it, would be "nasty, brutish, short"? 

Negation, then, has an objective reference. How are we to 
classify the "subjective failure" which is sometimes a fact of 
experience? Can we classify it as either affirmative or nega- 
tive, or does it, perhaps, fall outside this distinction? Let us 
consider. In every judgment, whether affirmative or negative, 
so long as we succeed in establishing contact with reality, so 
far as reality accepts our ideal suggestion, we have a sub- 
jective reaction — the reaction which we may roughly designate 
as satisfaction in our success. Failure, then, is something 
different. It is not our reaction either when we establish an 
affirmative relation, or when we establish a negative relation. 
It arises only when we do not succeed in attaching our float- 
ing idea to reality, when this remains a floating idea and we 
still do not know whether reality accepts it or no. We have 
asked our question and cannot answer it. Our attitude is one 
of painful suspense, with a certain sense of failure. Our sug- 
gestion obstinately refuses to leave the unsubstantial region 



112 APPENDIX 

of the imagination. Put simply, we do not succeed in making 
our judgment. We do not judge. The sense in which Sigwart 
and others take negation must be interpreted, then, as involv- 
ing, not negative judgment, but absence of judgment. That is 
a subjective failure, and results in the Socratic confession of 
ignorance. But we must not confuse it with the establish- 
ment of a negative relation between S and P in the objective 
world. Either we judge, or we do not judge. If we do judge, 
we judge something positive; we assert a relation r, whether 
the relation is mainly one of identity or mainly one of differ- 
ence. If we do not judge, that may represent a failure of 
ours, but we must not confuse ourselves by calling it nega- 
tion or negative judgment — for it is not judgment at all, 
neither affirmation nor negation. "When we think," asks 
Socrates, "do we think something, or nothing?" "Some- 
thing," is the answer. "And to think nothing means, not to 
think."i 

Is Negation Indefinite? — Negation, then, is objective in its 
reference. But there remains a further difficulty. When a 
scientist states that his results are "only negative," he is 
usually. not satisfied. Negative conclusions do have an objec- 
tive reference, but it is felt that they do not give us much 
information about the object to which they refer. "This is 
not Mr. Smith" does not do much towards establishing the 
identity of the Unknown. If we knew him to be Mr. Jones, 
that positive and affirmative knowledge would of itself be 
sufficient to rule out the possibilities of his being Mr. Smith, 
or Mr. Brown, or Mr. Robinson. As we sometimes say, there 
is only one thing which a thing is, but an infinity of things 
which it is not. Consequently, to establish a negative rela- 
tion merely touches the fringe of this "infinity," and does 
not always bring us much closer to what we desire to know. 
At best it does little more than narrow the field of enquiry, 
and its function is thus mainly preliminary to genuinely 
scientific work. It is for this reason that there seemed to be 
some truth in the theory of negation as failing to get into 
touch with objective reality. We know now that it does estab- 
lish contact, but apparently only with the fringe or outside 
edge of the subject. This is expressed by saying that negation 
is indefinite — i. e., indefinite in not stating the ground of the 

i Plato, Republic, 477 E. ff., Theaetetus, etc. 



NEGATION 113 

negation. An affirmative judgment, it is thought, would be 
more definite, and would state the ground of the affirmation. 

Consider the following instances: "This watch is not 
going," "He has not arrived," "Your letter did not reach me," 
"She was not there," "The medicine had no effect," "These 
cartridges did not explode," "Your orders can not be carried 
out," "He did not take the examination." In each of these 
cases the negation is objective in its reference, and is impor- 
tant. It establishes the fact that something is wrong But 
it leaves it an open question as to what is wrong. It is nec- 
essary to search further for the ground. Some spring may- 
be broken, one of the screws may be missing, the watch may 
require to be oiled, or I may merely have forgotten to wind it. 
He may have gone astray, his train may be late, he may have 
missed his train, he may have forgotten to start, he may have 
decided to stay away and break the appointment. The fact 
is established, but the explanation of the fact is still to seek. 

Let us examine further. The watch is not going — yet the 
springs are not broken, the screws are not out of place, it 
has not run down and remained unwound — perhaps the 
reason is to be found in the fact that it has not been oiled for 
many years. So too the automobilist, in searching for the 
causa malt when his machine will not work, goes through 
such judgments as "No, there is nothing wrong with the 
carburetor, nothing is wrong with the oil-feed, nothing is 
wrong with the ignition," etc., until finally he discovers "There 
is no gasoline." Every successive negation established nar- 
rows the field of enquiry, until at last — we have the reason, 
or at least enough of the reason for our immediate purposes. 
The watch does not go because it has not been oiled, the 
automobile refuses to move because there is no gasoline, the 
letter failed to reach me because it did not leave the writer's 
pocket, he did not take the examination because he was not 
prepared. 

These instances, however, prove more than we were antici- 
pating. The judgments which actually do express the ground 
(the watch has not been oiled, he was not prepared for his 
examination, etc.,) are not affirmative but negative. A nega- 
tive judgment can, then, after all express the ground. Or — to 
state our result in another form — negation is not confined to 
the "fringe" of a question. It can go straight to the heart of 



114 APPENDIX 

the matter. "This coat will not do, because there is not a 
button in place," "This composition receives the mark F, 
because there is no unity and no mass in it," "He missed 
every shot, because he did not understand how to use the 
sighting apparatus." In other words, negative judgments can 
be perfectly definite and explicit in stating the ground. "No, 
I won't lend you a dollar. Why? — Because you do not pay 
back what you borrow." "You can't thread that needle — the 
eye is not large enough for the thread." It is difficult even 
to imagine more explicit statements of the ground. 

It is not, then, impossible for a negative judgment to be 
perfectly definite. What are we to say about affirmative judg- 
ments? Is it impossible for them to be indefinite? Must they, 
one and all, state a ground clearly and unambiguously, or do 
they also vary from indefiniteness to definiteness? Is it only 
negative judgments which skirt the edge of a subject and 
gradually narrow it down? Is not the same true of affirma- 
tive judgments also? 

Let us consider a few instances. "There is a department of 
study called philosophy. There is a part of philosophy called 
logic. A certain part of logic is called the theory of judgment. 
A certain part of the theory of judgment deals with intellectual 
standards. Identity is one of these intellectual standards." 
Here we have affirmative judgments which progressively nar- 
row down a field of enquiry. It might, however, be questioned 
whether any of them could be called "indefinite." Let us pro- 
ceed, therefore, to consider a different type: "Pyrrhus, I say, 
the Romans can subdue." "A man, whose last name began with 
B, called to see you," "He was traveling in Germany, or some 
such country, at the time," "Someone has been here," "There 
are times when I sort of wonder whether anything is worth 
while," "I feel something, but it seems rather hazy." It is 
unnecessary to multiply instances. The conclusion is simply 
forced upon us, that affirmative judgments also can be indef- 
inite. 

We should, perhaps, note further that many judgments can 
be expressed easily and naturally in either affirmative or 
negative form. The emphasis shifts as the form changes, but 
the general meaning seems to remain much the same. "Don't 
lend him money — he is not to be trusted in money matters." 
The general meaning is much the same if we are told "he 
is untrustworthy in money matters." Let us consider further 



NEGATION 115 

instances: ''The patient is not yet strong enough — the patient 
is still too weak," "This coat is not long enough in the back 
— this coat is too short in the back/' "He is not feeling well 
— he is feeling ill," "I shall not be here tomorrow — I shall 
be elsewhere tomorrow," "That is not Jones — that is someone 
other than Jones," "This color is not purple — this color is 
different from purple." From such examples it looks as though 
our thought, whether superficial or profound, whether indef- 
inite or definite, can be expressed either affirmatively or 
negatively. Affirmation emphasises the identity-aspect, and 
negation the difference-aspect of our thought. As we have 
seen above, all thought has both aspects. It seems safest to 
conclude, then, that all our thinking has aspects which can 
be best expressed negatively, and other aspects which can be 
best expressed affirmatively, but that, as a matter of fact, all 
our thoughts can be expressed in either form, though one form 
will be more appropriate to certain situations, and the other 
form to other situations. 

Our final conclusion is, that our thought, whether definite 
or indefinite, has an objective reference, and that negation is 
as objective and definite as affirmation, and affirmation is as 
subjective and indefinite as negation — the two being related 
to one another as are identity and difference in our judg- 
ments. 

FOR FURTHER READING 

F. H. Bradley, Principles of Logic, pp. 109-120. B. Erdmann, 
Logik, (2nd Edit.), pp. 496-520. J. G. Hibben, Logic, Part I, chapter 
viii. Chr. Sigwart, Logic, Vol. I, chapter v. W. Wundt, Log Ik, (3rd 
Edit.), pp. 200-211. 

EXERCISES 

1. Are the fallowing judgments subjective rather than objective : 
Not a soldier discharged his farewell shot. This ribbon is not red. 
The train will not start for another ten minutes. God is not mocked. 
I never apologise. No combination of yellow and red will give blue. 
This conduct is not to be tolerated? 

2. Are the following judgments more indefinite than their affirma- 
tive counterparts : Never say die. Not another word ! Not a single 
match would light. No educated man would accept that statement. 
Julius Caesar never dreamed of the New World. My desk is not 
oak. This typewriter has not a blue ribbon. This electric light will 
not work. Nothing venture, nothing win. My father was not in the 
park at 10:15. 23547912 is not a prime factor? 



116 



APPENDIX 



579 and 732 do not 
Not more than one 



3. Point out the affirmative elements in the following : No real 
lady would aot thus. This material is not silk. We shall never get 
off this mud bank. I never dine before noon, 
make 1234. Black is not a positive sensation 
man in fifty will vote for that program. 

4. Point out the negative elements in the following : That Is 
blue. I have accustomed myself to wearing white ties. Two plus 
two makes four. Pompeius was known as "the Great" in his own 
life-time. He was thinking of taking a walk. The fire was growing 
stronger. We shall pay you a visit tomorrow. 



PART II. 
THEORY OF INFERENCE 



117 



CHAPTER XI 
THE GENERAL CHARACTERISTICS OF INFERENCE 

What are the Marks of Inference? — What do we understand 
by inference or reasoning? Perhaps we can best discover 
by examining a number of typical instances. "If Winnipeg 
is north of Minneapolis, and Minneapolis is west of Chicago, 
then Winnipeg must be northwest of Chicago, and Chicago 
must be southeast of Winnipeg." "If our guest tends to be 
gracious when he has celery for lunch, let us by all means 
lay in a large supply of celery." "If a bird in the hand is 
worth two in the bush, then two in the bush are worth one in 
the hand, and it is still an open question which I may happen 
to prefer." "If x^+y — xy=55, and x — y=5, it follows that 
x=10 and y=5." "If Mrs. Smith is my wife's mother-in-law, 
then — unless my mother has married again — my son's name 
must be Smith." "If I had $5.00 when I started out, and if 
I only spent 10c for carfare and $3.65 for dry goods, I cer- 
tainly ought to have $1.25 left." "If this piece of blue litmus 
paper turns red, that is a sure sign that the fluid before us 
is acid." "If oxygen and hydrogen are combined in the pro- 
portion of 1:2, the result is water." 

These cases are all fairly simple. For the sake of com- 
pleteness let us add a few which are more complex. "If the 
Minnesota team beat Wisconsin, and Wisconsin beat Chicago, 
and Chicago beat Illinois, then Minnesota ought to be able to 
beat Illinois." "If potatoes do well in Jones' garden, and the 
soil in my garden is like his, and these potatoes are like 
those which did so well with him, and if I am as careful a 
gardener as Jones, then I ought to be able to raise a good 
crop myself." "If the batteries are in working order, and 
the sparking plugs are all right, and the machine is well 
oiled, and the brake is off, and there is plenty of gasoline, 
then — if I can only get this self-starter to work — we ought 
to begin to move." "If my testimonials are all they should 
be, and if I look at my best and am not nervous, and if there 
is no other candidate with better testimonials or a better 
appearance, then I ought to get the position." 

119 



120 GENERAL CHARACTERISTICS OF INFERENCE 

Dependence. — Let us examine these various instances to 
discover what they may have in common, in order that we 
may realise, at least in a preliminary way, what are the most 
striking characteristics of inference. One such characteristic 
stands out with especial prominence. In every case we notice 
an "if . . . then," a "certainty," or a "following upon" 
which we may call "dependence." "J/ my testimonials . 
then I ought to be appointed." That is to say, the probability 
of my getting the position depends upon these conditions, so 
far as I know. An inference thus seems to be a kind of 
judgment which asserts that a conclusion x depends upon, 
or follows upon, a condition or premise a, and the typical 
/Orm of inference would thus appear to be "If a, then x," or, 
if we wish to do justice to the complexity of the cases, "If A 
is B, 8 is P."i 

Dependence then, or the following of a conclusion upon a 
premise or condition, appears to be one constituent or char- 
acteristic of all inference. Can we say, it is the fundamental, 
distinguishing feature of inference — or must we look further? 
Let us consider. We have stated that inference seems to be 
a kind of judgment which expresses dependence. Can we con- 
vert this and say that a judgment which expresses dependence 
is an inference? For this is one of the tests of a good defini- 
tion. Let us see. "My appointment depends upon certain 
conditions." "The direction of Winnipeg from Chicago is con- 
nected with the relation of both places to Minneapolis." "The 
surname of my son is definitely related to that of my father." 
"Water is H 2 0." These formulations of our thought all 
express dependence, some more clearly, others less clearly. 
They are all, then, judgments expressing dependence. But 
are they quite what we should call inferences? Hardly. They 
look more like what we should call statements, and we should 
draw a distinction between a statement and an inferred state- 
ment, even when the simple statement expresses dependence. 
The expression of dependence, then, is not the chief consti- 
tuent of inference, though it may be one of the characteristic 
features of reasoning. It follows, that, for the discovery of 
the fundamental features of reasoning, we must look further. 

Analytic Expansion. — The objection to the foregoing defini- 
tion was, that it attempted to reduce inference to a type of 

i This view Is represented especially in the work of Sigwart. See 
his Logic, Vol. I, chapter iii. 



ANALYTIC EXPANSION 121 

judgment, whereas it seems to be something wider. If we 
compare such a judgment as "My appointment depends on 
certain conditions," with the inference "If this condition, and 
that condition, and the other condition, are all realised, then 
I ought to be appointed," we see at once that, while both 
express the same meaning — i. e., have the same reference — 
the inference expresses it in a more expanded form. It repre- 
sents a more thorough-going analysis, as a result of which 
all the steps from which the conclusion follows are set in 
array as explicit conditions or premises.2 Let us take an 
example. "AB=BA." The form of statement is the same, 
whether it expresses an intuitive judgment — i. e., is reached 
by "simple inspection," — or whether it expresses the conclu- 
sion of a process of inference. But the man who has gone 
through all the steps3 has a much clearer and more reliable 
insight into the truth of the statement. He has not jumped 
hastily to the conclusion, but has a knowledge which is firmly 
based upon analysis, and such knowledge has been tested and 
examined, rather than left to first impressions. From this 
viewpoint the distinction between judgment and inference or 
reasoned knowledge is the difference between what we call 
"feminine intuition," i. e., trusting to unanalysed impressions, 
and reasoned knowledge based upon methodical analysis.* An 
inference is thus an analytically expanded judgment, and we 
may regard this characteristic as "analytic expansion." 

But if we accept this and look no further, shall we be alto- 
gether satisfied? Our view makes of inference an analytic 
refinement upon judgment, in such a way that, instead of 
stating roughly and in general terms that "S is P," we have 
analysed out the various factors involved, and know what it 
is in 8 and what it is in P which makes them stand to one 
another in this relation. That such analysis is of great value 
is beyond question. But, when all is said and done, are we 
not left just where we started? Have we succeeded in adding 
to the sum of our knowledge a single new idea? Our ideas 
are now far more clear and distinct. Our knowledge is highly 
polished and clear-cut, but— has it advanced a single step in 
a direction which could be called new? Have we discovered 

2 This view is represented especially in the work of Lotze. See his 
Logic, esp. §§ 97 ff. 

3 For the actual steps, see infra, chapter xxix. 

* Cf . R. L. Nettleship, Lectures on Plato's Republic, opening lecture. 



122 GENERAL CHARACTERISTICS OF INFERENCE 

anything hitherto unknown? Let us see. We know that 8 is P, 
and we know, rather more than less, why we think so. We 
have made clearer to ourselves the elements which together 
constitute the complex 8 and the complex P. But surely we 
knew all this before; not so clearly, perhaps, and not with 
such certainty, but still in the main we did know it — so that 
at the end we remain with the same sum of knowledge with 
which we started.^ Is this perfectly satisfactory as a account 
of inference? Does it not remain a puzzle how we could ever 
discover whether 8 might be Q or R or T — or indeed how we 
ever managed in the first place to hit upon the idea that it 
was P? But briefly, if this were all, or even the most impor- 
tant part of inference, inference is the analysis and classifica- 
tion of knowledge which we have somehow managed to dis- 
cover by some other means. But we have a suspicion that 
inference is a method of discovery, that it is one of the means 
of extending the field of knowledge and learning something 
which is new. Can we justify this suspicion? 

Novelty. — Let us ask then, whether a third characteristic 
of inference is not that it leads to something new\ or adds to 
sum of knowledge. Consider a few instances. The Abbe is 
chatting with the ladies. "Ah, ladies, my first experience in 
the confessional was terrible indeed. My first penitent was 
a murderer!" Soon after, their host entered the room. "Well, 
ladies, chatting with our good Abbe? Do you know, I was 
his very first penitent?" There can be no doubt that the ladies 
drew an inference which told them something new about their 
host — something which had not been told them either by the 
Abbe or by their host. The Abbe had spoken generally, with- 
out hinting at any names, and had merely emphasised the 
horror of his situation, as a young man, on being brought 
into relation with one who had committed so terrible a crime. 
The whole stress was on the shock to his delicate and 

5 The student of Latin composition will be familiar with this from 
e. g., "Bradley's Arnold/' where he learns in one exercise that the 
present tense can be used to express not only present time, hut time 
immediately past, time immediately future, and even time perfectly 
past (i. e., can he used for the imperfect, future, and perfect tenses), 
and finds in subsequent chapters that the imperfect tense can he used 
for the present, the perfect, and the pluperfect, the perfect tense can 
be used for the present, the imperfect, and the pluperfect. When he 
comes to the end of the (quite elaborate) account of how these tenses 
can be used, he really knows little more than he did before. He is, 
if anything, made far less certain which form of expression would be 
appropriate in a given case, as he has to choose between approximately 
three iforms, without really knowing which would be the best. 



NOVELTY 123 

untrained nerves, at meeting with a real murderer. The 
secrets of the confessional were not revealed, though there 
was, perhaps, a slight indiscretion in speaking of such things 
at all. So too their host does not tell them that he is a crim- 
inal. He is merely emphasising the many years that he and 
the Abbe have known one another. In fact, it was at the 
very outset of the latter's ecclesiastical career that they had 
become acquainted. The reference to the confessional is slight 
and general — one of the usual incidents of their religion — 
and the whole stress in on the many years in which he has 
been intimate with their good Abbe. The inference, however, 
certainly leads to something new — in fact to a startling and 
shocking discovery about their host's early life.6 

Let us take another instance. The new minister, in the 
course of one of his first sermons, happens to mention how 
young he was when he served in the Spanish-American war. 
"I was only eighteen at the time." Instantly every member 
of his congregation puts two and two together and discovers 
how old he is novo. This is new information. It is something 
which they wished to know, and which he did not tell them. 
He was merely emphasising the extreme youthfulness of many 
of "the boys" at the time of that service. His parishioners, 
however, compare dates and come to a conclusion which is 
an interesting discovery and satisfies their curiosity on that 
head. Inferences of this general type are of very frequent 
occurrence in our every-day intercourse, and are certainly to 
be met with in science also. Many great discoveries have 
been made by a trained scientist's putting two and two 
together in this way, and we may accordingly regard novelty 
as at least an extremely important element in inference.? 

Have we, in this characteristic, discovered the full nature 
of inference? Can we rest satisfied with a definition which 
tells us that inference is a form of reasoning which leads to 
the discovery of something new? Let us consider. Assume 
that all inference gives us knowledge which is new. But, we 
must still ask, is every process which gives us new knowl- 
edge to be regarded as inference? A sudden shoot of pain 
will produce knowledge which is new — it informs me that 
I have the toothache, that there is something wrong with my 

6 Cf. Royce, Sources of Religious Insight, pp. 94-96. The instance 
is from Hibben's Logic. 

7Cf. J. S. Mill, System of Logic, Bk. Ill, chapter ii. 



124 GENERAL CHARACTERISTICS OF INFERENCE 

tooth, and that perhaps I had better see my dentist. The 
last two statements, which refer to the cause of the pain, 
and the way in which it could be removed, would probably 
be considered inferences. But the knowledge that I have a 
pain in my tooth, or the toothache, while certainly new, would 
not naturally or usually be called an inference. So too with 
all simple judgments of perception. "It is raining," "How 
warm it is getting," "I am thirsty," "You look quite pale," 
"This tree is turning brown," — these judgments and a hundred 
others of similar type would usually be regarded as judgments 
rather than as inferences, as we can realise if we compare 
them with such statements as "The roofs are wet — it must be 
raining," "Look at the thermometer — how warm it must be 
getting," etc. And yet they certainly contain information 
which is new. In order to exhaust the nature of inference, 
then, we must look still further. 

Constructive and Systematic. — Let us consider. An infer- 
ence differs from a simple perception, though both alike may 
give us knowledge which is new. In what precisely does 
this difference consist? Perhaps mainly that in simple per- 
ception we just apprehend what is forced upon us, what affects 
us immediately in sensation, whereas in inference we go 
through some process which may, indeed, start from sensory 
data, but may lead far beyond what is present in sensation. 
This process consists in inferring or drawing or deducing a 
conclusion from premises, i. e., from previous knowledge, 
which may or may not be of an immediately perceptual kind. 
In perception I just see. In inference, my thought completes 
itself by passing through a more or less elaborate process 
which gives me a result which has been deduced or reasoned 
out, which follows upon something else, which is true and 
certain, if that from which it follows is true and certain. 
Two or more previously acquired pieces of information are 
put together in such a way that they lead to a tertium quid 
which is new. That is to say, inference is constructive and 
systematic. In the two premises we have fragments of a 
potential system. The process of inference seems to con- 
sist in putting together these fragments so as to realise 
in -our construction something more of the system of which 
they now form a part. The "something more" which our 
construction thus produces is the new information or conclu- 
sion. For example, from an arc of a circle we can construct 



SYSTEMATIC CONSTRUCTIVENESS 125 

the rest of the circle, by first discovering the center, and then 
applying the postulate for circle-construction. That is to say, 
we manipulate the given material in accordance with the 
laws of the particular system, and thus acquire new informa- 
tion which is true within that system. So to in the infer- 
ence "If Mrs. Smith is my wife's mother-in-law . . ., then 
my son's surname must be Smith," the conclusion can only 
be reached by constructing the system of relations of con- 
sanguinity accepted by present social conventions. So too in 
"If a — h = (x+y) (x — y), and a = x," it follows with 
mathematical certainty — i. e., it follows with certainty within 
the mathematical system — that b = y. This we can only 
discover by constructing the relevant portions of the system 
within which such algebraic relations are worked out. So 
too the calculation, in trigonometry, of the distance of a ship 
at sea is discovered by constructing the system of cosines 
and tangents which is appropriate to the special concrete 
situation. Inference is thus constructive and systematic^ 
and this characteristic is obviously of such fundamental im- 
portance that we might, in a preliminary way, define infer- 
ence as the discovery of new information by the construction 
of a system, or — as Mill graphically expresses it — by arguing 
(systematically) from the known to the unknown.9 

Conclusion — The General Characteristic of Inference. — Our 
conclusion, then, is that inference is (1) dependent, t. e., is a 
matter of "If . . . then," rather than of simple state- 
ment; (2) analytically expanded, i. e., is reasoned knowledge 
as opposed to an unanalysed impression; (3) novel, i. e., 
leads to a result which constitutes a genuine discovery of 
something new; (4) constructive and systematic, i. e., reaches 
its conclusion by constructing the relevant portions of a 
system of knowledge which is appropriate to the concrete 
situation. Put briefly, inference seems to be a process of dis- 
covery by constructing an appropriate system. 

But before we can advance from this preliminary sketch to 
a final view of inference, we must examine more in detail 
the four characteristics which we have discovered. This 
examination will be the task of the succeeding chapters. 

8 Cf. especially Bradley, Principles of Logic, pp. 255 ff. 

9 This is to be taken merely as a striking phrase. Cf. Schuppe, 
Erkenntnisstheoretisclie Logik, p. 260. Sigwart, Logic, pp. 360-362. 
How far, if at all, we can reason from the known to the unknown 
is considered below. 



126 GENERAL CHARACTERISTICS OF INFERENCE 

FOR FURTHER READING 

B. Bosanquet, Logic, Vol. II, chapter i. F. H. Bradley, Principles of 
Logic, pp. 235-239, 396-411. B. Erdmann, Logik, (2nd Edit.), pp. 
588-593. J. G. Hibben, Logic, Part I, chapter x. 

EXERCISES 

1. Point out the element of dependence in the following : You 
vote for F as captain, and I'll vote for your friend B as first lieuten- 
ant. Get a good lock for your car, unless you want to have it stolen. 
I didn't give Mm the order, because it seemed to me that he was 
trying to charge too much. 

2. Point out the element of analytic expansion in the following : 
If she be not fair to me, what care I how fair she be? If that is 
my car, I must run. Anyone who can put two and two together 

. must realise that sincere atheism is a self-contradiction. 

3. Point out the element of novelty in the following : If I spend 
$5.00 a month for rent, and $10.00 a year for books, and $30.00 a 
year for clothes, and other expenses in proportion, I ought to manage 
on about $450.00. If this is what education leads to, it's back to 
the farm for me ! If sunflowers, corn and mangel-wurzels grow as 
easily as that, it ought not to be much trouble to feed poultry. 

4. Point out the element of systematic constructiveness in the 
following : If you can't find time to do this typewriting for me, 
then I shall have to take it to a public stenographer, and shall 
probably have to pay quite a sum for it. If my train leaves at 6:30 
a. m., I shall have to get up at about 4 :30, in order to be ready in 
time. If he won't help me with my work, I shall refuse to help 
him with his. 



CHAPTER XII 

THE DEPENDENT OR HYPOTHETICAL NATURE OF 
INFERENCE 

Dependent Nature of Inference. — As we have seen, in infer- 
ence we draw our conclusion from premises. If x — y = 8, 
and we know that y = 2, it follows that x = 10. That is to 
say, the truth of x's being equal to 10 follows from, or depends 
upon, the truth of the premises. If the premises are cor- 
rect, then the conclusion holds good. If oxygen and hydrogen 
are combined in the proportion of 1:2, water results. In 
other words, the phenomenon called water results from our 
experiment only if the requisite conditions are fulfilled, or 
is dependent upon the fulfilling of those conditions. It is 
not true absolutely, but only on condition of the correct 
proportion being observed. This characteristic of the con- 
ditionedness of inferred truths is expressed by calling them 
"hypothetical." Water is not regarded absolutely, as water, 
but as the resultant of certain complex chemical conditions. 
Music is not regarded simply as music, but as an effect pro- 
duced by the intermingling of sound-waves in an order deter- 
mined by a number of rules, i. e., as resulting from the fulfil- 
ment of a whole complex of conditions. So too Taenia saginata 
is not treated simply as a certain kind of worm, but as a 
certain stage in a complex series of life-forms, each of which 
develops under certain definite conditions, and the whole 
series of forms can be brought to an end by interfering with 
any stage where the conditions admit of such interference. 

Inference, then, is hypothetical, or the conclusion is depend- 
ent on the fulfilment of certain conditions. Can we analyse 
further this element of dependence, and come to realise in 
what it consists, or how it is constituted? Let us consider 
a few cases. "If I delay any longer, I shall miss the car." 
"If the corn is planted too early, the seeds will rot." "If 
children persist in sucking their fingers, they must be pun- 
ished." What is it that I really judge in such cases? Do I 
judge that I shall miss the car, or that the seeds will rot? 

127 



128 DEPENDENT NATURE OF INFERENCE 

Hardly, for perhaps I shall hurry, and thus not miss the 
car; perhaps the corn will be planted later, in which case 
the seeds will develop normally. I do not, then, judge that I 
shall miss the car. What is it, in that case, which I do judge? 
Do I judge that I shall delay longer, or that the corn will be 
planted too early? Again, we must say, this can hardly be 
the case; for it may be otherwise, and the "if," taken strictly, 
leaves it entirely unsettled whether or no. I do not, then, 
judge either that the seeds will rot or that they will not rot. 
In other words, I make no simple judgment at all.i What is 
it that I do? I go through a process of thought which is 
complex, and draw a conclusion from premises. My judg- 
ment is, the seeds will rot if planted too early, I shall miss 
the car if I do not hurry, children must be punished if they 
persist in wrong-doing. My conclusion is thus a conditioned 
conclusion, and what I judge is essentially the connection of 
premises and conclusion. I establish a law of connection — 
the connection of ground and consequent, or of cause and 
effect. The dependence of the hypothetical judgment is thus 
the dependence of consequent upon ground. 

Kinds of Dependence: (A) From Cause, (B) From Absence 
of Cause. — The dependence is thus the dependence of an 
effect or consequent upon a condition. Let us proceed to ask, 
in what ways and to what extent are consequences depend 
ent upon conditions? Let us take a few cases. "If I expose 
myself unduly, I shall catch cold." The consequence is here 
clearly dependent upon the functioning of certain general laws 
of health. Suppose the condition realised, suppose I do expose 
myself unduly. In that case, so far as my knowledge goes,2 I 
shall certainly catch cold. So far, so good; this is reasoning 
from cause to effect. But let us now suppose, on the other 
hand, that the condition is not realised — suppose I wrap myself 
up carefully. How about the consequences? Do I, or do I not 
catch cold? As we commonly understand the laws of health, 
it would follow that, so far as cold-from-exposure is concerned, 
I do not catch cold. In other words, we can, in such cases, 



i The view in the text is opposed to that of Sigwart, who regards 
both if-clause and then-cla,use as expressing judgments. But it seems 
inadvisable to treat them as judgments, since they are certainly not 
judged. 

2 The connection here is only "empirical" — i. e., a matter of imper- 
fectly analysed and imperfectly understood experience. The "law" 
does not always hold good, but so far as I know, I expect it to work. 



KINDS OF DEPENDENCE 129 

argue both positively and negatively. If the condition is real- 
ised, the consequent is realised, and if the condition is not 
realised, then the consequent is not realised either. We can 
argue from presence or absence of cause to presence or absence 
of effect. The rotting of seed-corn, for instance, depends upon 
the wetness present in the soil. If the soil is wet, the seeds 
rot; if the soil is not wet, the seeds do not rot. If I wait 
longer, I miss the car; if I do not wait, but hurry, I catch 
the car. If children persist in wrong-doing, they must be pun- 
ished; if, however, they amend their ways, they must not be 
punished. If you work, you may some day amount to some- 
thing; if you don't work, you will never amount to anything. 

These are all instances in which the connection is a matter 
of empirical law. Experience shows that the connection holds, 
as we say, in the long run. But we do not have precise 
insight into the condition, as we do in the so-called exact 
sciences. Do we, then, find a different result in the exact 
sciences? Let us see. "If a triangle is equilateral, it is equi- 
angular." If it is not equilateral — if, e. g., it is scalene — is it, 
or is it not, equiangular? It is not equiangular, and the case 
is similar to what we discovered in the empirical cases. "If 
(a-\-b) be multiplied by (a — b), the result is a2 — &2." if, how- 
ever, (a+b) be not multiplied by (a — b) — if, e. g., it be divided 
by it, or if it be multiplied by (c — d) — the result is not a^ — b?. 
"If 32 be added to 57, the result is 89." If, however, 32 be not 
added to 57 — if, e. g.. it be subtracted from 57, or be added to 
41 — the result is not 89. In other words, in the exact sciences, 
as well as in our more empirical thinking, if our thought suc- 
ceeds in penetrating to a law which holds good, then we can 
say: — (1) if the condition is realised, the consequent is real- 
ised, and (2) If the condition is not realised, neither is the 
consequent. If A is B, S is P; and if A is not B, S is not P. 

(C) From Effect; (D) From Absence of Effect. — Let us 
consider further. A relation of dependence is two-edged. If 
A is in relation to B, B is also in relation to A. So far we 
have considered only what we can infer when the condition is, 
or is not, realised. Can we, however, start at the other end, 
and ask, given the consequent or effect, is it possible to draw 
any safe conclusion about the ground, or cause? Or again, 
granted that the consequent or effect has not been realised, 
can we infer, perhaps, that the ground or cause has not been 
realised? Let us consider. Suppose I have caught cold. This 



130 DEPENDENT NATURE OF INFERENCE 

is an effect. Can it be inferred — if it be an exposure-cold — 
that I have unduly exposed myself? As we commonly under- 
stand the laws of health, undoubtedly, Yes. Suppose, on the 
other hand, that I have not caught cold. Can it be inferred 
that I have not exposed myself? Not perhaps with the same 
degree of certainty, for the statement of the empirical law in 
question is not quite exact, and people do sometimes expose 
themselves without suffering the consequences. But on the 
whole, my immunity from colds is fair evidence that I have 
taken reasonable care of myself, and it would usually be 
argued, that if I have no cold, I have probably not been expos- 
ing myself unduly. Let us consider the next case. If the 
seeds have rotted, can we infer that the soil has been wet? 
Gardeners would say, Yes. If however, the seeds do not rot, 
but develop normally, can we infer that the soil was not wet? 
Or at least not unduly wet? This seems a little less certain 
— for the same reason as before, viz., that the law is only 
empirically and imperfectly known — but on the whole it also 
would be answered in the affirmative. If the seeds show no 
traces of rot, it would be inferred that the soil had not been 
wet. So too in the other cases. If I miss the car, it can be 
inferred that I delayed too long. If I catch it, it can be 
inferred that I did not wait too long. If the children have 
been punished, it can normally be inferred that they have been 
doing something which they ought not to have been doing. If 
on the other hand, they have not been punished, that is at 
least presumptive evidence that they have committed no seri- 
ous offences. Similarly if a man's success is pronounced, it 
would usually be inferred that he must have worked hard to 
earn it. If, on the other hand, he never amounts to anything, 
it would as a rule be inferred that he had not worked hard. 

These cases being all empirical, the degree of certainty with 
which we can argue from consequent to ground, or from effect 
to cause, varies in the various cases. But on the whole we 
are certainly convinced that where the consequent is realised 
— where, that is, we have an effect — the condition or cause 
must have been realised also, than that where the effect is 
absent the suspected cause must also have been absent. Let 
us now review the cases taken as examples of exact science. 
If a triangle is equiangular, can we argue that it must be 
equilateral? Yes, certainly we can. If, however, a triangle is 
not equiangular — e. g., suppose it obtuse-angled — is it to be 



KINDS OF DEPENDENCE 131 

inferred that it cannot possibly be equilateral? Yes, again, 
quite certainly. Let us take the next case. If the result of 
multiplying (a + b) by a second factor be a2 — &2 } can we infer 
that the second factor must have been (a — b) ? Yes, certainly. 
If, however, the result was something else — e. g., ax — y% — can 
we infer that the second factor was not (a — o) f Most cer- 
tainly we can. Our conviction depends upon our insight into 
the law in question — the divisor-dividend-quotient relation — 
and we can be in no possible doubt either in the positive, or in 
the negative case. So too, if we are acquainted with the laws 
of addition and subtraction, we know that if 32 plus something 
adds up to 89, the second element in question must be 57, and 
that if the result is not 89 — but is, e. g., 65 — we can infer with 
mathematical certainty that 32 has not been added to 57. In 
other words, in the more exact sciences as well as in our more 
empirical thinking, if our thought has succeeded in penetrat- 
ing to a genuine law of connection — of ground and consequent, 
or cause and effect — then, if the consequent or effect is real- 
ised, we can argue that the ground or cause must have been 
realised: and if, on the other hand, the consequent or effect 
is not realised, we can infer that the ground or cause cannot 
possibly have been realised. 

Conclusion. — Expressed generally, our conclusion is, that if 
we are sure of the law which connects A-B and S-P, so that 
we can say £'s being P depends on A's being B, then we can 
argue from our law of connection in all the four ways discov- 
ered above, viz., (1) If A is B, it follows that S must be P; (2) 
if A is not B, it follows that & cannot be P (so far as our 
knowledge goes) ; (3) if & is P, it follows that A must be B; 
(4) if £ is not P, it follows that A cannot be B. That is to 
say, we can reason from ground to consequent, or from con- 
sequent to ground, from cause to effect, or from effect to cause, 
either positively or negatively, with reasonable certainty — the 
degree of certainty being precisely proportionate to the degree 
of our insight into the law of connection in question. 

Further Consideration. — It is perhaps advisable to dwell fur- 
ther on the imperfect cases — in which we have not entirely 
succeeded in attaining a genuine law of connection — in order 
to see what can be inferred in such cases. Believers in appa- 
ritions, for instance, state as a hypothetical law that an abnor- 
mal event, such as a murder, tends to leave traces of itself in 
the locality — e. g., in the form of vibrations which perma- 



132 DEPENDENT NATURE OF INFERENCE 

nently modify the structure of the walls or furniture — so that 
when a sensitive person is in the neighborhood, these traces 
will affect the imagination of such a person, in such a way 
that he will see a visual image or "ghost." The cause is here 
the murder, and the effect is the apparition. But compare the 
two inferences: — (a) If a murder has been committed, then 
a sensitive person will see an apparition, and (b) If a sensi- 
tive person sees an apparition, then a corresponding crime 
must have been committed. Which of these two inferences 
would meet with the wider acceptance? The great majority 
of believers would feel more certain of (b) than of (a), and 
would justify their belief by reasoning that an apparition is 
an effect, and that, since every effect has a cause, an abnormal 
effect probably has an abnormal cause. In such cases the argu- 
ment from effect to suspected cause has more weight than 
the argument from cause to effect. Let us now consider the 
negative side of the relation, (c) If no murder has been com- 
mitted, the sensitive person will see no apparition; (d) If 
the sensitive person sees no apparition, then no murder has 
been committed. Which of these two inferences seems the 
more probable? To a majority of the "authorities" in this 
field, (c). would seem more reasonable than (d). That is to 
say, in such cases we could argue from the absence of the 
cause to the absence of its suspected effect, but could not so 
certainly infer from the absence of the effect to the absence 
of the suspected cause. 

Let us take another instance of such imperfectly analysed 
thought. In the case of certain diseases, it is believed by 
physicians that if the patient is to recover, he must desire to 
get well. The suspected cause is here the "will" of the patient, 
and the effect hoped for is his recovery. Let us see what can 
be inferred, (a) If he earnestly desires to get well, he may 
be cured, (b) If he is cured, he must have wanted to recover, 
(c) If he does not wish to get well, he will not recover, but 
will probably die. (d) If he does not recover — or if he dies 
— that is a proof that he cannot have really desired to recover. 
Not one of these inferences is certain, but (a) would be 
thought slightly more probable than (b). and (c) would be 
thought slightly more probable than (d). That is to say, in 
such cases as this, the argument from cause to effect seems 
more probable than from effect to suspected cause, whether 
we are reasoning positively or negatively. It is, however, only 



CONCLUSION 133 

fair to add that no physician would risk his reputation by sup- 
porting any one of these inferences. The probability, in such 
cases, is usually realised after the event. 

Conclusion. — Is there any one infallible rule for inferring in 
this field — the field of "popular," half-analysed thought? Let 
us see. In the apparition case, it seemed reasonable to infer 
from the presence of the effect, or from the absence of the 
cause. In the mental healing case, it seemed allowable to 
argue from the presence, or from the absence, of the cause, 
but not from the presence of the effect. That is to say, both 
cases agree in permitting an inference from the absence of 
the suspected cause to the absence of the suspected effect. 
These instances thus agree with the seed-corn and car-catching 
cases, at least in the single particular of admitting an infer- 
ence from the absence of the cause. Arguments from (1) 
presence of cause, (2) presence of effect, (3) absence of effect, 
appear to be admissible in certain cases, inadmissible in others. 
That is to say, the only inference which holds good invariably 
in the instances before us is the argument from absence of 
cause. Can we then state as our conclusion that in such half- 
analysed thought it is at least always permissible to argue 
from the absence of the cause to the absence of the suspected 
effect? Let us consider yet another instance. "If the locomo- 
tive ran over him, he must be injured, perhaps fatally." What 
kinds of inference can here be drawn? (1) From absence of 
effect: if he is uninjured, it is scarcely credible that the loco- 
motive can have run over him. (2) From presence of cause? 
Yes, with a fair degree of certainty. If the locomotive has 
run over him, we are pretty sure that he cannot possibly be 
uninjured. (3) From presence of effect? Let us see. If by 
"injured, perhaps fatally" we refer (as of course we do) to 
the kind of injuries received in being run over, the experts at 
the inquest would infer from effect to cause, and their infer- 
ence would tend to be accepted. (4) Finally, can we argue 
from absence of cause to absence of effect? In other words, 
does this case agree with the others in permitting this kind 
of inference, or must we conclude that there is no one definite 
rule applicable to such reasonings? If the locomotive did not 
run over him, can we argue that he is not injured in that kind 
of way? Some logicians — e. g., John Stuart Mill — would assert 
that an effect may be produced by a "plurality" of causes, and 
that from the absence of any one cause we cannot reason to 



134 DEPENDENT NATURE OF INFERENCE 

the absence of the effect. For the effect might have been 
brought about quand meme, by any one of the other possible 
causes. For instance, he may have escaped the locomotive, but 
may have fallen beneath a street-car or an automobile. Is 
this objection to be taken seriously? Or is it not rather too 
superficial to merit attention at the present day? We do not 
infer from his not having been run over by the locomotive 
that he is, e. g., alive and well at the present moment. That 
would be to go far beyond our information. We argue only 
that he has escaped injury of a particular kind — the kind 
caused by locomotives. He has escaped locomotive-injuries. 
About theoretically possible injuries from other sources not a 
word has been said. Our conclusion, then, is that however 
the admissibility of the other modes of inference may vary in 
empirical cases of cause-effect reasoning, the argument from 
absence of cause to absence of effect is reasonable, and fur- 
ther, that there is a tendency for us to feel, in all such cases, 
that if the connection in question is at all valid, there must 
be some degree of evidence for all four modes of inference. 

Hypothetical Versus Categorical. — One further point remains 
to be discussed. Inference, as we have seen, is hypothetical, 
conditioned — i. e., has an "if" in it. It might be thought that 
an unconditional form of statement — "categorical" as it is 
named — i. e., a direct statement without even the suggestion 
of an "if" about it — would be more valuable, and thus should 
be the goal of inference. Compare, for example, the two forms 
of expression: — (1) "1/ that street-car coming round the cor- 
ner is yours, you must hurry." (2) "That street-car is yours; 
hurry!" There is no i/-ness about the second, or categorical, 
form of expression. It is unhypothetical, does not admit of 
doubt or hesitation, but demands instant action, The hypo- 
thetical form does not tell us whether or no — it leaves the if 
in full force, i. e., it leaves the question still open. The cate- 
gorical form, on the contrary, leaves no room whatever for 
questioning or deliberation. It tells us outright that the fact 
is so. It thus seems to go further than the hypothetical form, 
and it might reasonably enough be asked, which form should 
be our ideal, and which attitude it is, on the whole, wiser and 
more logical to cultivate, — the hypothetical, or the categorical. 

Let us consider a little further. The categorical form really 
seems to have more to offer than the hypothetical. For it 
does not end with an unanswered question, but is direct and 



HYPOTHETICAL VS. CATEGORICAL 135 

straight-forward, and, as we have seen, leads immediately and 
by the shortest path to action. It resembles the bedside man- 
ner of the practising physician, which cuts across half a hun- 
dred hesitations and disputed questions and boldly orders a 
definite line of treatment. It is, in fact, in general, the .atti- 
tude of applied science and common sense, and, like them, 
betrays a certain impatience with the questionings, with the 
sceptical, impartial, judicial attitude of the theoretician, the 
"pure" scientist. Practical life needs quick decisions. Ques- 
tions must be settled, one way or the other, and settled at 
once. Theory is all right in its place — but its place is the 
research laboratory or the research publication, and not in 
the office or the home. What the practical man needs is 
results, definite concrete rules which can be used, and not 
eternal questionings which lead nowhere. 

On the other hand, the practical attitude seems somewhat 
dogmatic. To cut short deliberation and enquiry is, in the 
last resort, unprogressive, and leads to mental stagnation. 
The hypothetical attitude is concerned with discovery, with 
the establishment of laws, with the exact analysis of phe- 
nomena and study of their conditions. Not unduly under the 
influence of practical considerations, its interest is in enquiry, 
in testing, investigating, finding out what is to be learnt in 
the sure school of a science based upon experience. Not leap- 
ing to conclusions, but studying problems; not deciding too 
soon, but weighing arguments; not rapid, but very sure, and 
above all, progressive. It is the attitude of theory, of study 
and science, of logic and philosophy, as opposed to mere com- 
mon sense and an interest confined to the immediate needs 
of practical living. Which attitude should be cultivated 
depends upon our character — on the kind of persons we are 
and the kind of persons we wish to be. For modern logic, 
the hypothetical interest in scientific method seems more val- 
uable than the categorical, rule-of-thumb method of the half- 
trained practitioner, though it is not denied that, in its place, 
this too is valuable. Method versus results; deliberation ver- 
sus action; progressiveness versus complacency. Which is the 
more valuable? Which attitude do we ourselves choose? 

Concluding Summary. — Let us now put together what we 
have discovered in the present chapter. There are, generally 
speaking, two kinds of knowledge: — (1) scientific, in which 
we have attained a degree of insight into the working of some 



136 DEPENDENT NATURE OF INFERENCE 

law; (2) popular knowledge, the field of the practical man 
with his rule-of-thumb methods and his love of categorical 
statements. The first kind is more hypothetical, and is inter- 
ested in discovering the particular ifs upon which certain con- 
clusions depend. The second kind does sometimes throw its 
results into the if form, but is usually more categorical. In 
the hypothetical cases, if we have succeeded in discovering 
some law, we can argue or infer from the law in four typical 
ways. We can reason from the presence or absence of the 
cause or ground to the presence or absence of the effect or 
consequent; or, vice versa, we can argue from the presence 
or absence of the consequent or effect to the presence or 
absence of the ground or cause. If our thought has only par- 
tially succeeded in its analysis, and we are not quite certain 
of our suggested law, we cannot argue with the same degree 
of certainty. The ideal is, here also, all four forms of infer- 
ence, but in practice we have found only one which does not 
vary — viz., the argument from the absence of the cause to the 
absence of the effect. This has seemed always reasonably 
admissible, but in proportion as our knowledge is greater and 
our thought more strict, even the popular forms of inference 
tend to allow all four types of reasoning.3 

3 As a practical illustration of what we have discovered in the 
present chapter, we might state that if it is true that the workings of 
a law lend themselves to the four typical inferential forms, then it 
will also be true that wherever we can make all four inferences with 
reasonable certainty, that is a safe test of the validity of the law in 
question, and that where we are unable to draw all four inferences 
with equal certainty, that is a safe indication that we have not yet 
succeeded in discovering the law in the case in question. Cf. the 
rule re the convertibility of a definition, infra, chapter xxvii. 

FOR FURTHER READING 

F. H. Bradley, Principles of Logic, Bk. I, chapter ii. J. G. Hibben, 
Logic, Part II, chapter xii. Ohr. Sigwart, Logic, Vol. I, pp. 326-338. 

EXERCISES 

1. Assuming the following inferences to be correct, what infer- 
ences can be drawn from ground to consequent, or from consequent 
to ground,* and which of these seem the more probable : If he writes 
to me again, I shall not read his letter. If the lawn-mower won't 
cut, I shall send and have it sharpened. If the car has no gasoline, 
of course it won't start. If this sand were only cleared away, it 
would be grand. If you want to be an engineer, you will have to 
study and go to college? 



EXERCISES 137 

2. Assuming the following inferences to be correct, what infer- 
ences can be drawn from ground to consequent, or from consequent 
to ground :* If you will not help me put the car into the garage, 
I shall not take you out riding with me again. If this history book 
says so, it must he true. If the engine is really off the rails, it will 
be necessary to get a derrick for it. If you love me, you will love 
my dog. If you are a good shot, you should score 100% at that 
range ? 

3. Assuming the following inferences to be correct, what infer- 
ences can be drawn from ground to consequent, or from consequent 
to ground:* If x = 5 in the equation 2x — 3xy -f- 4y = 10, then 
f .3= 1. If the plane figure in question is such that it is rectilineal, 
and a closed figure, and such that any of its exterior angles is equal 
to the sum of the interior opposite angles, the figure in question 
must 'be a triangle. If the quotient is 61, and the dividend is 305, 
the divisor must have been 5. 

* i. e. t both from the presence of ground (or consequent), or from 
the absence of ground (or consequent). 



CHAPTER XIII 
THE ANALYTICAL CHARACTER OF INFERENCE 

Nature of Analysis. — So far we have considered the differ- 
ence between the categorical and hypothetical viewpoints, and 
have seen that inference or reasoning is hypothetical rather 
than categorical. Let us now proceed to compare statements 
and inferences from a new viewpoint, in order to bring out 
what we took to be the second main characteristic of infer- 
ence, viz., its analytical nature. 

The practical man never analyses, if he can help it.i He 
just acts, and acts in accordance with habit and routine. For 
most of the purposes of life — which are instinctive — little 
analytical reasoning is required. Most of our ends are easily 
attained, and a conventional attitude of mind as well as a 
conventional appearance — what we call the professional man- 
ner — carries us safely through most of the social contingen- 
cies which present themselves. It is, in fact, only when things 
cease to run smoothly, when something goes wrong, that 
analytical thought is called into play. A man who finds the 
door refuse to open behaves, at first, precisely like a trapped 
animal, such as a dog, cat, or monkey. He pulls, pushes, kicks, 
and knocks, and makes a fuss generally. It is only when this 
method fails that his attention is directed to investigating the 
cause, and to taking measures to have the conditions reme- 
died — e. g., by telephoning to the janitor or locksmith, before 
descending by way of the fire-escape or window. The occasion 
for inference is thus the breaking down of our customary 
methods of precedure before novel circumstances. These neces- 
sitate the adoption of new methods especially adapted to the 
new occasion — require a new analysis of the situation, a sub- 
stitution of analytical investigation for the practical rule-of- 
thumb method of "common" sense. 

So much for the occasion of inference. The way in which 
we actually reach our solution is still, in the main, the method 

i Of. W. B. Pillsbury, Fundamentals of Psychology, chapter xi (on 
Reasoning). 

138 



NATURE OF ANALYSIS 159 

of trial and error. Various associations are aroused, tested 
mentally, and rejected, until at last there comes into our minds 
one which fits the case and leads to action. Explicit analysis 
takes place only when we direct our attention to the chief 
elements in the problem, and to the chief steps of a solution 
which will be just to them all. 

In this way, then, we analyse practically a practical situa- 
tion. Let us proceed to consider a case which is less imme- 
diately practical. I am reading Kant's ''Critique of Pure Rea- 
son," and am doing my best to understand the "psychological" 
part of the "transcendental analytic." I find that a great deal 
of the constructive work of knowledge is performed by the 
"imagination," but when I try to make clear to myself just 
what imagination does, especially as compared with sense on 
the one hand and understanding on the other, I find myself 
baffled. I try all the ways out which suggest themselves. Has 
imagination, in Kant's sense, anything to do with mental 
imagery? — That doesn't seem to fit in with its "transcen- 
dental" functions. Is it, perhaps, like the creative imagination 
of the poet? — That also does not seem very helpful. I consult 
the explanatory literature which is at my disposal — but that 
seems to play fast and loose. At one moment imagination 
seems the same as sensory perception, at another it exercises 
much the same functions as understanding — with the peculiar 
qualification that it is "blind." I give up this way of trying 
to learn. Unmethodical guesses, or looking up, at haphazard, 
literature which was obviously written without any feeling 
for my particular problem, gets me nowhere. I decide to find 
out for myself, if possible. There is only one way to find out, 
and that is, by exhaustive analysis of the situation itself. I 
make a collection of all the passages in which the term is 
used. I then collect leading statements about sensory expe- 
rience, and about the work of understanding. I proceed to 
classify the data with which I have thus furnished myself, 
putting together all statements which seem to bear on some 
one point — e. g., (1) the "blindness" of imagination, (2) its 
"synthetic" function, (3) the relation of reproductive to pro- 
ductive imagination, (4) "schemata" as distinguished from 
images, etc. — until I have exhausted all the distinguishable 
points which appear to be treated in Kant's writings. I then, 
very gradually, find what he seems to have had in mind, and 
my problem is solved. 



140 ANALYTICAL CHARACTER OF INFERENCE 

Here again, although the material is very different, the gen- 
eral method of dealing with the situation seems much the 
same as before. I do not analyse until the rough and ready 
method of trial and error breaks down. Here also my analysis 
seems to be simply an attempt to appreciate, one by one, the 
various distinguishable features of the situation, in the hope 
that, if I take them one at a time, some ray of illumination 
may dawn upon me, and I shall be helped out of my diffi- 
culty. It differs, however, from the old attempt by being 
methodical and exhaustive, rather than haphazard and at ran- 
dom. It tries all the ways, rather than those which chance to 
present themselves to me, and thus leads to some sort of sat- 
isfaction. For if I have tried all the ways, I know that I have 
done my best, and that my non-success is not a mere matter 
of chance— which a little perseverance might remedy. 

Special Features of Analysis. — Let us focus our attention a 
little more closely upon certain features of our analytical 
method. In the first place, we do not bring in hypotheses ex 
machina. To find our solution we split up into its elements 
the situation which is before us, and act accordingly. If I 
wish to learn to play music, it will never do just to read books 
on "the three B's," Bach, Beethoven, and Brahms, but I must 
patiently and methodically practise scales, chords, ana pas- 
sages, until I can solve the technical problems presented in 
the particular sonata or fugue which I wish to perform. There 
are also musical problems to be solved, which also will require 
specialised studies appropriate to the occasion. We have to 
remain very close to our data. Thus no one would dream of 
inferring that Socrates must die on the general ground that 
"all men are mortal, " but for the specific reasons that the 
Athenians have condemned him to death, that he is in the 
condemned cell, that the fatal morning has arrived, that he has, 
in fact, drunk the hemlock and it has begun to take effect. So 
too no botanist would infer that plants grow upwards because 
they love the sun, or even because they have a positive helio- 
tropism and negative geotropism, but would dissect the various 
stem-cells, and would show the precise way in which certain 
starch-granules rest normally upon the sensitive protoplasm at 
the bottom of those cells, and thus furnish a delicate mech- 
anism for appreciating the influence of gravitation, analogous 
to the statocysts of primitive animals. So too the X-chromo- 



SPECIAL FEATURES OF ANALYSIS 141 

some and the mitotic subdivision of cells were discovered, not 
by general reasonings, or by haphazard guesses, but by patient 
and methodical experimentation with the various factors 
shown, by histological analysis, to be present in the concrete 
situation. It is thus the situation before us which is the 
direct and sole subject of our analysis. 

A second question concerns the "elements" to which we 
analyse. These vary in the various concrete situation. If we 
are studying language, it is in units which are grammatical 
or phonetic, that our analysis terminates. If it is plane 
geometry that we are studying, our analysis terminates in 
lines and points. If it is history, then we end up with the 
various types of data which can be regarded as furnishing 
"testimony," whether documents, archaeological remains, or 
what not. We do not find tones in histological analysis, or 
centrosomes in musical analysis. That is to say, our units 
or elements differ qualitatively according to the qualitative 
differences of our various universes of discourse. But in spite 
of these differences — differences so great that we can seldom 
hope to argue from what takes place in one field to what may 
be expected to happen in another field — there are certain 
important respects in which our elements agree. Analysis as 
such always involves interference with the concrete situation. 
It is split up. It ceases to exist in its natural form. What is 
irrelevant for our purposes is discarded, and only what is 
strictly to the point is taken into the focus of attention. This 
involves a certain artificiality, and our elements are all 
abstract, intellectualised entities, bloodless concepts. The trail 
of the intellect is over them all. 

This gives to the products of analysis a certain unity which 
we should never anticipate from what we have seen of the 
qualitative differences of the various universes of discourse 
— a unity derived, of course, from the intellectual nature of 
analysis itself. The products of analysis are, for instance, 
almost always numerable, and almost always parts of wholes; 
and they always have a (varying) number of other character- 
istics in common. From this unity of form, it sometimes 
comes about that the instruments forged by intelligence to 
deal with one type of situation can, as a matter of fact, be 
utilised, with but slight changes, to deal with another type of 
situation. Our analytical methods thus become schematised. 



142 ANALYTICAL CHARACTER OF INFERENCE 

Just as the artist has a body of working schemes2 for repre- 
senting a man, a tree, or a house, just as, in social intercourse, 
we acquire generalised ways of approaching other people with 
what we call "tact," — so the trained scientist has at his com- 
mand a body of generalised ways of dealing with his kind of 
problems — a method of analysis which can be applied easily 
and with but slight modifications to fit all sorts of special 
cases. A logician like Bosanquet3 or Royce can apply the 
schemes of biological analysis to logic. A metaphysician like 
Spinoza can apply quantitative methods to the concept of 
Deus sive Natura — and there seems to be no way of deciding 
how far this can be done. "Transgressing into another kind," 
as Aristotle named it, has become a fine art, and, as a matter 
of actual practice, we all recognise that "scientific method" is 
much the same, whatever the special material to which it is 
applied. 

A fourth feature of our analytical method is, that it does 
not, and can not, go beyond its data. Schematised and gen- 
eral as it is, it can never extract, in the way of elements, 
more than is present to be extracted. It splits up the con- 
fused and concrete situation, omits what is irrelevant, and 
takes up what is relevant. These elements stand out far 
more clearly after the analysis than before, as in Aristotle's 
analysis of friendship^ or Windelband's analysis of Plato.s 
But they were there all through, embedded in the concrete 
situation, and only awaiting our analysis for their discovery. 
This is so obvious, that it would be unnecessary to emphasise 
it, if it were not so incessantly sinned against. To recon- 
struct Locke's thought in the light of CondillacG or of Kant? 

2 Of. F. C. Ayer, The Psychology of Drawing, esp. pp. 8-9, 74-75, 
100, 159. A "scheme" is a method tfor representing in an image, as 
e. g., the method of representing pleasure or grief in the human coun- 
tenance by curving the eyes and mouth upwards or downwards, respec- 
tively. 

3 Bosanquet's book is "Logic or the Morphology of Knowledge." 

4 See Aristotle's Nicomachean Ethics, Bks. VIII-IX, with the intro- 
duction of Sir Alexander Grant to Bk. VIII. 

5 Windelband, in his small volume on Plato, by treating in separate 
chapters Plato as a Teacher, as a Philosopher, as a Theologian, as a 
Prophet, and as a "Social Thinker," has given an impression of amaz- 
ing lucidity — such as without that analysis would have been impos- 
sible. 

6 Cf. e. g. Victor Cousin, La Philosophic de Locke. 

7 Of. e. g. the treatises comparing Locke and Leibniz written by 
G. Hartenstein and by G. v. Benoit — to mention only two out of a 
goodly company. 



ANALYSIS AND INTUITION 143 

is just as illogical as to reconstruct Kant in the light of 
Hegel,s or to read monistic idealism^ or Freudian psychology 10 
into Shakespeare. The analysis of Locke's thought should 
lead to elements which are Lockian; the analysis of Shakes- 
peare to elements which are Shakespearean, just as the analy- 
sis of space leads to elements which are spatial, or of time to 
elements which are temporal. Otherwise we are embarking 
upon the hopeless quest of explaining everything in terms of 
something else — i. e., in terms of something which is not it — 
which is the reductio ad absurdum of such explanation. Our 
analysis must, then, restrict itself to what is given, and must 
not attempt to read into its data something which is extrane- 
ous and strictly irrelevant. 

Analysis and Intuition. — So far we have seen that the 
analytical method, in splitting up the given situation, (1) 
keeps as close as may be to its data, (2) is schematic or 
slightly more general than the specific occasion seems to 
require, (3) leaves us with elements which are somewhat 
artificial, and yet (4) were there, embedded in the concrete sit- 
uation, only awaiting methodical analysis to become evident. 
It remains to compare it with a method which employs no 
explicit analysis, but reaches its conclusions by simple inspec- 
tion — the intuitive method. 

Compare for example, (1) "His character must be good, for 
he has consistently acted in this, that, and the other kind of 
way," and (2) "His character is good — I couldn't say why, but 
I just feel sure of him." The analytical inference is less cer- 
tain than the intuition, less confident of itself. It sums up 
the evidence, and rests the responsibility for the conclusion 
upon the certainty of that evidence. The intuitive judgment 
says nothing about the evidence — there is no appeal to logical 
reasoning, for the person in question feels sure — he "just 
knows." So too we might compare, (1) "This way must be 
shorter than that, for if you count up the number of blocks, 
you will find that there are two more blocks that way," and 
(2) "This way is shorter than that — It just seems so some- 
how." The intuitive person seems less hesitant, seems to feel 

8 Cf . e. g., the accounts of Kant given by Kuno Fischer and by 
Edward Caird. 

9 Cf. A. C. Bradley, Shakespearean Tragedy. 

10 Cf. Ernest Jones, "The Oedipus-complex as an explanation of 
Hamlet's mystery," tn. American Journal of Psychology, Vol. XXI, 
1910, pp. 72-113, and Psychoanalysis. 



144 ANALYTICAL CHARACTER OF INFERENCE 

less in need of the longer way round to his conclusion. In 
some cases the longer way — that of analytic inference — seems 
less applicable. Compare, e. g., (1) "This picture must be 
finer than that, for (a) you can see what this is intended for, 
(b) it is drawn according to the rules of perspective, and (c) 
the colors are bright and clear," with (2) "This picture is 
finer than that — I couldn't give any reason, and I don't need 
to — it is. a matter of the aesthetic intuition. Either you have 
it or you have not. If you have it, you don't need to argue 
about it — you just know." 

Both intuition and analysis arrive at conclusions — but only 
analysis states the evidence on which the conclusion seems to 
depend. Intuitive thought is far more common than analysis. 
For most purposes it is sufficiently correct, and for some pur- 
poses — e. g., in judging works of art — it seems more correct. 
But we may reasonably ask, which of the two attitudes of 
mind is it wiser to cultivate? On the one hand we have the 
widespread belief in intuition. "Give your decisions," said 
the experienced judge to the new appointee, "they will prob- 
ably be right. But keep your reasons to yourself — they are 
sure to be wrong." So too our modern psychologists!! tend to 
regard all motivation as welling up out of the depths of our 
subconscious nature, while all the specious reasons which we 
give for our conduct tend to be discounted as mere "ration- 
alisations," i. e., as disguises by which we hide our motives 
from ourselves and others by letting them appear only as 
clothed in language appropriate to the system of ideals recog- 
nised by the conventions of social usage. On the other hand 
we have the equally widespread belief in reflection, analysis, 
deliberation. To which of these two opposed beliefs ought we 
to yield the more loyal allegiance? 

By intuition we mean, in general, that attitude of mind by 
which we put ourselves in the other fellow's place, and try to 
feel as he would be feeling. It is a matter of feeling rather 
than of reasoning, and seems to be immediate, structureless, 
simple — just knowing. It is unreflective and unmethodical, 
and feels a certain distrust of elaborate arguments, as of 
instruments which somehow come between us and what we 
are studying — which distort and falsify our view, warping our 
judgment until we don't really know just what we do believe. 

ii Cf. e. g., W. James, Varieties of Religious Experience, and Bernard 
Hart, Psychology' of Insanity. 



ANALYSIS AND INTUITION 145 

We feel the value of intuition especially in ethics, in aesthetics, 
and above all in religion. It is especially in these fields that 
we trust our intuitions most completely, and feel most distrust 
of reasoning. "Metaphysics," says Bradley — himself a meta- 
physician — "is finding bad reasons for what we believe by 
instinct."i2 

On the other hand, in mathematics, in chemistry, in biology, 
and in the sciences generally, we should never dream of trust- 
ing to intuition. In these fields analysis, patient, methodical 
experimentation, with all the powers of reasoning as well as 
of observation which we possess, is universally admitted to be 
the only feasible method. So too in much of our every-day 
life we should never think of trusting intuition. Do I have 
an "intuition" that this is my street-car, that the rain will be 
only a shower, that the business deal which I have just com- 
pleted is going to turn out a magnificent success? Yes, I do 
have intuitions in this field, but experience has taught me to 
distrust them, and to replace them by analysis and experiment. 
Scientific method, in business as well as in purely scientific 
study, reliance upon analysis and reasonings verified by 
methodical appeals to experience, is the only safe guide here. 

What are we, then, to conclude? Are we to believe that in 
practical life and in science, analysis should be our rule, but 
that in all which concerns the inner life, — art, goodness, and 
religion, — intuition — unanalysed feeling — is a trustworthy 
guide? There is, of course, no doubt that this is precisely the 
solution which most men accept — the system of watertight 
mental compartments — one for the office, another for the 
church; one for the opera-house, another for home life. In 
business relations, in scientific research, they analyse and 
infer. Nothing is taken upon faith. In the realm of ideals 
and "values," faith, trust, intuition is their guide. We must 
ask, however, not whether this attitude is commonly accepted, 
but whether it is wise, consistent, logical, whether it is not 
rather the source of our unprogressiveness in the things of 
the spirit, in the essentials of civilisation, while in externals 
we seem to have advanced by leaps and bounds. 

Let us consider. Intuition is not radically distinct from 
analytical reasoning. Both often reach the same conclusion, 
and often take a similar path. The only difference is, that for 

12 Cf. F. H. Bradley, Appearance and Reality, preface. Cf. also 
B. Russell, Problems of Philosophy, pp. 39-40. 



146 ANALYTICAL CHARACTER OF INFERENCE 

intuition the reasons are not made explicit, are not weighed 
and tested, but just followed. All the emphasis is placed 
upon the conclusion — the way by which that conclusion has 
been reached remains out of sight. Our choice, then, is 
between (1) accepting conclusions with unbounded faith, but 
without careful weighing of the evidence and setting forth 
the grounds which might influence a reasonable man, and (2) 
only drawing inferences after the fullest consideration and 
analysis of all the facts before us. So stated, there can be 
no longer any hesitation. Reflective analysis as a method 
for the conduct of life is immeasurably superior to unreflect- 
ing intuition — wherever and whenever such analysis can be 
fruitfully applied. The reason why it has not been accepted 
as the sole reasonable method is because the inner life cannot 
easily be subjected to scientific analysis, as well as the pres- 
sure of practical needs, which so often confine our attention 
to the external things of life. But there can be no doubt 
that, as our psychological insight gradually develops, we shall 
be able to extend the method of analytical inference over more 
and more of the inner life, and that the progressiveness which 
is so marked a feature of the fields to which that method has 
hitherto been applied, will continue to invade the new terri- 
tory also. Wherever applicable, then, analysis, deliberation, 
weighing all the evidence, bit by bit, is a safer guide than 
intuition, and the reasoning, deliberative, analysing habit of 
mind is the one to cultivate. 

Conclusion. — Our conclusion is, then, that inference is 
analytical, i. e., does not treat the material before it as a 
simple unanalysable whole, to be reacted to by" an intuition, 
but as a complex situation which must be split up into its 
elements. Such inference remains always close to the con- 
creteness of the situation, and examines the elements, one by 
one. As produced by an analysis which has torn them from 
their living context, such elements are somewhat artificial. 
But they are, after all, not created by our analysis, but dis- 
covered by it, and are clear and helpful in enabling us to 
understand the concrete situation before us, when we attempt 
to put it together for ourselves. Wherever this method can 
be applied, analysis is superior to intuition, and the analytical 
habit of mind is the one which should be cultivated. 



EXERCISES 147 

FOR FURTHER READING 

F. H. Bradley, Principles of Logic, pp. 414-415. 

EXERCISES 

Compare the working of the intuitive method with the method of 
analytic expansion in the following situations : (a) In seeking a 
lodging in a strange town, (b) In dealing with a case of sickness, 
(c) In estimating the value of "popular" music as opposed to the 
music of Bach, Beethoven, and Brahms, (d) In accepting the tenets 
of a particular religion. (e) In investing one's savings in stocks, 
(f) In estimating the ethical value of charity. 



CHAPTER XIV 
NOVELTY IN INFERENCE. 

The Problem.— 2 + 2 =4. 2 + 3 = 5. This procedure is 
typical of all inference. We put together two or more prem- 
ises and the resultant conclusion is an item of information 
derived from neither premise alone, but from both taken 
together. Let us take a more complex example. 2X4 — % = 
7%. The number of possible premises — i. e., the number of 
distinct items of information which can be combined to yield 
a single conclusion — is theoretically unlimited. Any addition 
sum is an inference which furnishes us with information 
derived from all its premises, and expressing, from a certain 
viewpoint, the whole truth concerning those premises, how- 
ever numerous they may be. So too with statistical informa- 
tion. The arithmetical mean, in conjunction with the probable 
error, furnishes us with a kind of telescoped information as 
to the behavior of a large group, however many its members. 
A simple curve can tell us at a glance how students at Cornell 
or Harvard tend to be marked by their instructors.! A differ- 
ent, but equally simple, curve can inform us of the rate at 
which practise makes perfect.2 Both curves, however, though 
simple, express the result of innumerable distinct premises, 
and are, in fact, valuable in direct proportion to the number 
of cases which they sum up. So too a chemical formula or 
botanical law may express briefly and clearly the result of 
years of patient observation and experimentation; a poem or 
picture may sum up the experiences of a lifetime; and a phil- 
osophical speculation may express the soul of humanity. 

The problem before us in the present chapter is to ask 
how far such information is novel. That it is attained by 
methodical analysis of the premises, we have already seen. 
It remains to ask whether -what we obtain by summing up, 

i See Finkelstein, The Marking System in Theory and Practise, 1913. 

^ For some recent work in this field, see J. Peterson, Experiments in 
Ball-Tossing ; the Significance of Learning Curves. Jour. Exper. 
Psych., Vol. II, pp. 178-224. 

148 



SENSORY NOVELTY 149 

or by putting together, our premises is something which we 
already possessed, something which was ours all the time, 
or whether it is in any strict sense new. As Mill expresses 
it, can we "argue from the known to the unknown"? That 
is to say, can any logical manipulation of what we know, by 
any possibility lead us beyond what we know — extend the 
bounds of knowledge, and raise the veil which yet conceals 
the unknown from our eager vision? 

Sensory Novelty. — Let us consider for a moment. There 
are two sources of knowledge, (1) sense-perception, and (2) 
intelligence. So far as sensory experience is concerned, 
there can be no question that the information with which 
we are furnished through these channels is essentially novel. 
Color, sound, taste, touch, smell — an experience deprived of 
these would be poor indeed, and direct experience of these 
qualities is furnished us by the senses alone. No logical 
manipulation of sensory data — however intelligent that manip- 
ulations — can give us a new sensation. That is beyond the 
possibility of logic. That veil, at any rate, cannot be raised 
by the intellectual function of inference. Are we to conclude 
from this that the function of intelligent inference is, after 
all, to accept data derived from another source, and to proceed 
to classify? Are we to believe that sense-perception alone 
is the source of novelty in our experience? Are we to accept 
the view that intelligence can combine, analyse, and shift the 
positions of sensory data relatively to one another, but that 
to add to our positive knowledge is beyond the power of 
intellect? In other words, is the desiderated extension of the 
bounds of knowledge purely a matter of sense-perception, and 
is inference restricted to the organisation, to the re-arrange- 
ment of contents which cannot be altered, and above all can- 
not be increased by any logical manipulation whatever? 

For instance, I do not know whether there will be any 
mail for me today. Will inference help me? I turn over the 
probabilities in my mind. I do what I can with the knowl- 
edge which is at my command. I analyse it, turn it over and 
over, alter its arrangement by looking at it from different 
angles of approach. But do what I will, any conclusion to 
which I can come remains only probable. "There may oe 
a letter from X or Y." The only way in which my lack of 

s Cf. Hume's suggestion to the contrary, Enquiry into Human 
Understanding, Section II, last paragraph but one. 



150 NOVELTY IN INFERENCE 

knowledge can be converted into actual knowledge, is here 
by sense-perception. The postman's ring, followed by actual 
receipt of the letter, is in such cases the only satisfactory 
evidence. Shall I receive a certain appointment? Again I 
make use of all the knowledge at my disposal. I turn over 
and over what I know about myself and about the other candi- 
dates. I bring to bear all that I have heard of the disposition 
of the man with whom rests the final decision. Still, there 
is a gap. I do not know enough to feel certain. The only 
satisfactory evidence is, here again, by sense-perception — the 
receipt of an official notice of my appointment. Again — is 
the liquid before me an acid or an alkali? My knowledge 
tells me that if it is the one, it will turn blue litmus paper 
red, and if it is the other, it will turn red litmus paper blue. 
But I do not know which of these ifs will be realised. My 
knowledge does not reach far enough, and no amount of infer- 
ence will stretch it so as to bridge over the gap. The only 
reasonable thing to do is to dip in a piece of blue (or red) 
litmus paper, and see, by actual sense-perception, what takes 
place. Then, and then only, shall I know. These and a thou- 
sand similar instances serve to illustrate the value of observa- 
tions and experimental appeal to sensory experience, over 
arm-chair theorising. 

Intellectual Novelty. — It looks, then, as though observation, 
the appeal to sense-perception, is essential in discovering 
information which is new. And yet, before coming to a final 
decision, let us examine a different group of cases. I have 
a thousand dollars. I wish to invest profitably, and yet 
safely. There are two Government loans, both redeemable in 
three years, but the one pays 5,% interest and sells at par, 
while the other pays 4% interest, and is selling at 92. Both 
are equally safe. The only question is, which investment is 
the more profitable? I do not know. If I could find out with 
certainty, I should be acquiring information of the utmost 
importance to me. Would it also be newt It would at least 
be welcome news — novel in the sense that I do not know it 
now. If I could find out, there would be an addition to what 
I know. It might even turn out to be novel in the sense of 
unexpected. I may, in fact, be on the point of making an 
unwise investment. Perhaps, then, we can safely regard 
such information as new. And yet, no one doubts that this 
information can be acquired, and acquired by processes of 



INTELLECTUAL NOVELTY 151 

inference familiar to any mathematician. And further, a 
study of the analytical method examined in the preceding 
chapter should reveal the fact that such inference is restricted 
to the re-arrangement of contents which themselves remain 
unaltered. It looks, then, as if it must be possible, at least 
in some cases, by logical manipulation of given contents, to 
obtain knowledge which is reasonably regarded as novel. 

Let us take another case. I wish to know what some writer 
means by a technical expression peculiar to him — e. g., what 
Locke understands by "simple mode" or Plato by the term 
"idea." I have in each case a vague notion, derived from 
grasping the author's meaning, as best I can, as I read through 
his works. But my notion tends to change with each new 
instance of the term in question, and, in short, the evidence 
is so conflicting, that the only safe conclusion is, that I do 
not know what is intended. I cannot put it together and make 
one thing out of it. If I could really discover what the author 
means, I should acquire information which I certainly do 
not possess at present. I should add to my knowledge, The 
result would be new. It might also be novel, in the sense of 
unexpected — perhaps even as contradictory to the view which, 
in my present state of ignorance, seems least unreasonable. 
How can I find out? Mere sense-perception will not tell me. 
The instances are far too numerous, and the viewpoints far 
too complex, for that. I collect all the instances — which may 
be regarded as given contents, not to be altered in the course 
of the investigation. Then, by classifying these data in such 
a way that all which bear upon this point or upon that are put 
together, and every case which is irrelevant to the point at 
issue is excluded, I find that I can gradually settle one dis- 
puted point after another, until in the end I am able to formu- 
late a hypothesis which is just to all the facts, and in short 
gives me the information which I was seeking. I have thus 
discovered something new, and have discovered it by proc- 
esses of inference which were confined to re-arrangement of 
contents which remained unaltered throughout.* 

Let us take yet a third case. I am playing a game of chess, 
and am reasonably familiar with the moves and conventional 
gambits. At one stage of the game, no amount of inference 
could tell me, or anyone else, who is going to win. We must 

4 Cf. Lodge, The Meaning and Function of Simple Modes in the 
Philosophy of John Locke, 1918. 



152 NOVELTY IN INFERENCE 

fight it out and see. But at a later stage, my opponent sud- 
denly says, "Mate in four moves." I know enough about the 
game to see that I am seriously endangered, but I can not 
see that I must necessarily lose, whatever I do. I move. One, 
counts my opponent, as he also moves. I move again. Two, 
he counts. I look again. Yes, now I also can see that a check- 
mate in two more moves is inevitable. From my knowledge 
of the moves and from the position of the pieces on the board, 
I see that there are only a few moves which are possible for 
me, and that which ever of these I take, I must assuredly 
fall a victim in two more moves, provided that my opponent 
continues his attack. In this case my inference gives me 
knowledge. 

So far, then, we have seen that information which is new 
can be derived in two ways. There are some cases in which 
sense-perception alone can suffice, and no amount of theoris- 
ing, or re-organising what little knowledge we have, can 
be substituted for it. There are other cases in which sensory 
experience alone seems to be useless, and where the re-arrang- 
ing of what we know leads to information which is both 
important and new. It should be clear from an earlier chap- 
ters that both sensory and intellectual elements enter into 
the acquisition of any and every sort of knowledge. So that 
the question which now faces us is: How is it, that in some 
cases inference helps us to knowledge, while in others no 
amount of "theorising" leads anywhere? 

The Field of Relations. — To this question there are two 
answers. In the first place, admit that sense-perception alone 
is the source of certain kinds of knowledge — viz., knowledge 
of sense-qualities such as red, warm, hard, painful, etc., — still, 
there are other kinds of knowledge of which intellectual per- 
ception alone seems to be the source. A knowledge of straight 
lines and of circles — i. e., demonstrative knowledge based 
upon figures which are ideally perfect — seems to go beyond 
what sense-perception gives us. These geometrical figures are 
constructed in conformity with intellectual demands, rather 
than somehow taken from sensory experience; for in fact, 
it is very doubtful if ideally straight lines, for instance, have 
ever been met with in sensory experience. So too arithmetic, 
the knowledge based upon the relations of the elements of 

5 Chapter X. 



THE FIELD OF RELATIONS 153 

the number-series 1, 2, 3, . . . seems to transcend what 
we meet with in sense-experience. These units, each one of 
which is, from the viewpoint of quantity, ideally equal to 
every other, which extend in a progressive series from zero 
to infinity, in the plus or minus direction — are also intellectual 
constructions in accord with intellectual demands. Here also 
sense-perception plays a role which is at least subordinate. 
So too with the a, &, c, the x% and 2Z 2 of algebra, with the 
cosine alpha and tan theta of trigonometry — in a word, with 
mathematical relations generally. These all furnish us with 
information which is of great importance for life and for 
science, and which is also undoubtedly new. And — what is, 
perhaps, surprising — the mathematical sciences demand, and 
receive, very little aid from sensory experience. The knowl- 
edge of mathematical relations, then, seems to arise less from 
sense-perception than from intellectual construction and intel- 
lectual perception. 

So also with other branches of knowledge. "Conclusions 
drawn from premises which are true, are themselves true," 
"Entities related to the same entity are related to one another," 
"Every event has a cause," "If things-in-themselves are 
unknowable, then it is impossible to know that they are 
unknowable," etc.® To put it shortly, knowledge of relations 
appears to arise from intellect rather than from sense, whether 
such relations are mathematical, physical, logical, or what 
not. Knowledge of qualities is furnished us by sense-percep- 
tion; knowledge of relations by intellectual perception. 

While knowledge of relations is thus not derived from 
sense-perception, it must not be supposed that it has no appli- 
cation to the sensory field. A man who was born blind, but 
has studied physical and psychological optics, including, for 
instance, the theory of color-vision, can draw inferences which 
are perfectly correct within the field of color-vision, although 
as a matter of direct, personal experience, the blind man can 
never verify his own deductions by the appeal to sensation. 
His thought is, of course, moving in the realm of laws, i. e., 
of intellectually apprehended relations, and the accuracy with 
which this can be done, even in the complete absence of the 
corresponding sensory experiences, can be recognised when 

6 For further instances, and a discussion of such "apriori knowl- 
edge," Cf. Bertrand Russell, Problems of Philosophy, esp. chapters 
vii-viii. 



154 NOVELTY IN INFERENCE 

we study the writings, e. g., of Helen Keller, which abound in 
sense-imagery, although this can have only a symbolic signifi- 
cance for her. So also a comparative psychologist can write 
intelligibly about peculiar sense-experiences of certain ani- 
mals, where their sense-organs are very different from ours, 
and their sensations can be apprehended only symbolically 
by us. So too many short-sighted persons make up for their 
sensory deficiencies by using their powers of inference to a 
greater degree, and to some extent can, as they say, see with 
their intelligence rather than with their eyes. All knowledge 
of this type is, however, really given us by inference from laws 
and relations, and not by direct sensory experience. 

Latent Knowledge. — The second answer to our question is 
also concerned with relations, but is not so indifferent to the 
presence of sensory experience. Let us consider a few cases. 
If I know that acid turns blue litmus paper red, I can apply 
my knowledge in a particular case, and thus discover whether 
the liquid before me is or is not acid. The appeal is here 
to sense-perception — but to a sense-perception organised so as 
to supply an answer to an intellectually prepared question. 
I arrange or organise my data in a particular way. This is 
a matter of intellectual construction. I then observe the 
result which follows upon my construction. I have not added 
anything to the data, the contents before me, but have merely 
altered their order or arrangement, i. e., their relations to 
one another. By interfering with their relations to one 
another, e. g. y by dipping the litmus paper in the liquid, I 
set them working upon one another in such a way that they 
themselves produce a result which I observe. 

Let us take another instance. I wish to discover the mental 
age of a child suspected of being backward. I apply the Binet 
tests up to six years, seven years, eight years. In the tests 
for the eighth year, the child breaks down. He is also unable 
to perform the tests for the ninth and tenth years. I conclude, 
on this evidence, that he has a mental age of seven years. 
The security of this conclusion depends partly upon the 
experiences which have been summed up in the Binet scale, 
partly on the carefulness with which I have examined the 
child. The summing up of experiences which has determined 
the order and interrelation of the tests has been a matter of 
intellectual construction rather than of sensory perception. 
The behavior of the little child resembles the behavior of the 



LATENT KNOWLEDGE 155 

litmus paper in the acid test — it is something which is 
observed, and then interpreted in the light of the law. 

In such cases I discover information which is new, but 
is not confined to the realm of relations. I discover it by 
manipulating data, by changing their relation to one another, 
including some and excluding others, introducing a certain 
order, approaching nature in the attitude, not of a mere pupil, 
but of a judge, who determines what questions shall be asked 
and compels the witnesses to reply to those questions. Do I, 
however, always get an answer — i. e., does this method always 
furnish me with information? We must admit that it is not 
uniformly successful. Just as no judge can legitimately 
extract from a witness more than that witness knows, so no 
scientific method of manipulating data can extract from those 
data more than is there to be extracted. The evidence must 
in some sense be there, awaiting only the proper method for 
its discovery. 

Arguing to the Unknown? — So far we have seen that novelty 
in the case of inference is either a matter of restriction to a 
particular field — the field of relations — or, if inference leads 
to discoveries within the field of sense-experience also, this is 
brought about by some re-organisation of out experience which 
renders explicit sensory elements which were somehow there, 
but in a latent form — i. e., such re-organisation clears the way 
for observation. We should, perhaps, note that in the case 
of relations also, these come to be apprehended as a result 
of some reconstruction of our experience. Such reconstruc- 
tion, then, is present in both cases. The only difference 
between the two cases is, that in dealing with relations we 
are dealing with "form ,, -elements of our experience, while in 
sense-perception we have to do with "contenf'-elements. 
Neither form nor content is found alone, but the form is 
always the form of the content, and the content is always 
found in a particular form. Thus, in reasoning with reference 
to a triangle drawn on the board, a mathematician deals only 
with the "triangularity" features of the figure, with the 
geometrical relations of lines and angles ideally considered. 
But in addition to the triangular form, there is always a 
sensory content also — e. g., the chalkiness of the lines, their 
position on this particular black-board, the time of day, etc. 
The mathematician restricts himself to the field of mathe- 
matical relations, and neglects the sensory features as such. 



156 NOVELTY IN INFERENCE 

But in many cases in geometry, simple sensory inspection 
and direct sensory comparison of unanalysed figures will sug- 
gest to us the idea that two given triangles are probably 
equal, even when we are deficient in respect of that insight 
into relations on which the mathematical proof properly 
depends. It is, then, in the apprehension of elements hitherto 
unapprehended, whether such elements are of relational or 
sensory nature, that inference, so far as we can at present 
see, consists, and we are now in a position to answer our 
main question in this chapter, viz. How far our conclusion 
gives us information which is strictly new, or — as it is 
expressed by Mill — whether we can argue from the known to 
the unknown. 

We have, perhaps, by this time a suspicion that knowledge 
attained by careful inference must in some sense have been 
there all along, awaiting the proper construction to become 
visible to us. And in the case of discoveries within the field 
of sensory experience, we have already seen that this must 
be the case. We cannot construct a new sensation, but can 
only clear away obstacles, or take a new viewpoint, and thus 
come to discover what was there to be discovered. The 
case of relations, however, has not been adequately considered. 
Can we, in such cases, argue to the "unknown"? Let us con- 
sider a typical instance. Suppose I discover that it is possible 
to construct, on any side of any triangle, a parallelogram equal 
in area to parallelograms of any size whatever constructed 
upon the other two sides of the triangle. This was something 
which I used not to know, something which I should, perhaps 
have thought difficult, if not impossible, before I went through 
the proof J In going through the proof, then, which leads to 
a result so remarkable and unexpected, do I at any place argue 
from the known to the unknown? Let us see. 

Let ABC be any triangle, and let BDEA be any parallelo- 
gram on the side AB, and AFGC any parallelogram on the 
side AC. It is required to construct upon the third side BC 
a parallelogram equal in area to the sum of the parallelograms 
BE, FC. 

Construction. — Produce DE and GF to meet in H. Join HA 
and produce it to meet BC at K. Parallel to KH, draw BI and 

7 This "problem" was solved by Porphyry (5th Cent. A. D.) For 
the "proof" whi£h follows, I am indebted to the late Professor Cook 
Wilson, of Oxford. 



LATENT KNOWLEDGE 



H57 



D 



H 



K 



CJ, to meet DE and GF in I and J respectively. Join IJ. 
Then shall BIJC be the parallelogram required. 

Proof. — (1) To prove that BJ is a parallelogram. Because 
BH is a parallelogram, BI=AH; and because A J is a parallelo- 
gram, AH=CJ. Therefore, since each = AH, BI =CJ. And 
they are by construction parallel. Therefore, (by joining IC 
or BJ) it can be shown that the opposite sides I J, BC are 
equal, and that the opposite angles of the figure BJ are equal. 
That is to say, the figure BIJC has been proved to be a paral- 
lelogram. 

(2) To prove that BJ == the sum of the parallelograms BE, 
FC. Because BE, BH are parallelograms on the same base 
BA and between the same parallels BA, DH, therefore they 
are equal in area. Similarly, IK and BH are equal in area. 
Therefore, since each = BH, BE = IK. Similarly it can be 



158 NOVELTY IN INFERENCE 

shown that CF = JK, for each = CH. Therefore the whole 
parallelogram BJ = the sum of the parallelograms BE, FC. 

That is to say, upon BC, the third side of the triangle ABC, 
a parallelogram has been constructed which is equal in area 
to the sum of the parallelograms on the other two sides. 

Q. E. F. 

In the above figure we have constructed something which 
we did not previously know could be constructed. That is 
to say, we have really discovered something which was 
unknown by us. Have we, however, at any point in the pro- 
cedure, taken the "inductive leap," and gone beyond our knowl- 
edge by arguing to the "unknown"? Let us see. Our whole 
reasoning is based upon the known truths concerning paral- 
lelograms, as applied to the figure before us. The construction 
which gives us the particular figure allows us to apply our 
knowledge in a way in which it was, perhaps, never applied 
before, and thus to obtain an insight which is novel. But 
our procedure could not strictly be described as arguing to 
the unknown, as reasoning from something which we do know 
to something which we do not know. Our argument con- 
sists throughout in making clear to ourselves facts which are 
already implicit in what we know, facts which are present 
in our knowledge, but remain latent, awaiting the appropriate 
construction to become clear to us. We remain on terra firma 
the whole time, and take no "inductive leap" to the unknown. 

Could we perhaps say — to shift our ground — that arguing 
from a particular experiment with this single representative 
of the class "triangle" to all future triangle-experiences, or 
to all possible triangle-experiences, is arguing from something 
which we now know (this particular case) to something which 
we do not know (the "possible" cases, which we have not 
yet experienced)? Certainly not. The argument is not con- 
cerned with the "here" and "now," but is based upon insight 
into the nature of the triangle and the parallelogram as such. 
It is insight into the non-temporal realm of mathematical 
relations, and the question of time, whether past, present, 
or future, is strictly irrelevant. If I really grasp the proof. 
I have, in grasping it, apprehended the interrelations of such 
figures for any triangle, and we may safely conclude that, so 
far as insight into relations is concerned, we never argue 
from the known to the unknown, but always make explicit 
something which is implicit, i. e., something which is already 



EXERCISES 159 

contained in what we know, and is merely awaiting the proper 
method of construction to make it explicit and clear to us. 

Conclusion. — Reasoning from the known to the unknown, 
then, is impossible. Our inference can never take a leap and 
somehow transcend its data, the premises with which it starts. 
This must be abandoned as a chimera, as an attempt to get 
something out of nothing. Inference is always a matter of 
analysis, of disentangling something which is in some sense 
present — present, i. e., in the sense of awaiting discovery, 
awaiting the application of some method which will disen- 
tangle it and make it plain. This method of analysis, the 
method of disentangling in question, is what we understand 
by inference, and the so-called "novelty" of inference con- 
sists, not in somehow adventuring into realms unknown, but 
in so analysing and re-organising our experience as to let us 
see our way where, without such aid, we were at a loss. 
Analysis has been already considered. The other feature of 
inference, the construction which makes discovery possible, 
remains to be investigated in the succeeding chapter. 

FOR FURTHER READING 

B. Bosanquet, Logic, Vol. II, pp. 8-9. F. H. Bradley, Principles 
of Logic, pp. 419-429. 

EXERCISES 

Consider, in the following cases, how far the "discovery" is really 
novel: (1) By looking up a date in a reliable history book, I discover 
the date, which I did not know before. (2) By mixing approximately 
equal amounts of blue and yellow on the color-wheel, I discover that 
they make, not (as I expected) green, but gray. (3) By practising 
carefully, passage by passage, I find I can gradually learn to play 
Liszt's "La Campanella" — which I had always thought impossible for 
me. (4) By drawing a curve, I find that the center of a ladder which 
slides down the side of a house, describes the arc of a convex circle 
— whereas I had previously supposed it would have been a concave 
curve. (5) By eating porridge, I discover that it tastes good — where- 
as from its optical appearance I had always supposed it would not 
taste good. (6) By the use of a little trigonometry, I discover how 
far distant a certain ship is from the ship on which I am. 



CHAPTER XV 
THE SYSTEMATIC CONSTRUCTIVENESS OF INFERENCE 

Examples. — Add one to one. It makes two. Add one to two. 
It makes three. If we have grasped the principle, we can 
now add any number to any other number, or indeed can 
multiply any number by any other number. We can also 
easily learn to subtract and divide, with any numbers, or 
indeed with any quantities a, ft, c . . . n, whatever. The 
whole of arithmetic and algebra can be constructed from 
these simple operations. 

Take a ruler and place it upon a sheet of paper. With a 
pencil against the edge of the ruler, draw a line. If we have 
grasped the principle, we have learnt to draw any number of 
straight lines. Take a pair of compasses and describe an arc 
of a circle. If we understand the principle of the instrument, 
we can describe circles of any radius. Incidentally we under- 
stand that, by keeping the compasses open with the same 
radius, we can mark off equal portions along either straight 
lines or circumferences of circles. With these three simple 
premises, let us proceed to construct something difficult — 
e. g., a regular polygon such as a pentagon. 

To construct a regular pentagon: Draw any straight line 
AB, and on it mark off five equal divisions, AC, CD, DE, EF, 
EG. With center A and any radius, describe an arc HI J, 
cutting AB in 1 With center G and the same radius (AI), 
describe an arc HKJ, meeting HIJ in H and J. Draw a 
straight line joining H and J, and cutting AG in L. The line 
AG is thus divided into two equal portions AL, LG, and we 
now know how to bisect any straight line. With center L 
and radius LA (or LG), describe a circle. On the circumfer- 
ence of this circle, with compasses open to the extent AC 
(or CD, DE, etc), mark off equal portions AM, MN, NO, OP. 
Join in straight lines AM, MN, NO, OP, PA. The resulting 
figure is the regular pentagon required. If we have grasped 
the principle of this construction, we now know how to con- 
struct a regular heptagon, nonagon, or w-sided polygon, and 

160 



INFERENTIAL CONSTRUCTIVENESS 161 

indeed, can in principle construct the whole of plane and solid 
geometry, and even the meta-geometries. 

Let us leave mathematics, and consider life. Reflect upon 
the egoism of childhood, and its negation by the altruism 
of adolescence. Note how both alike are negated by the 
mature man, who, by living through both and finding both 
unsatisfactory, gradually rises to a level of ethical develop- 
ment which is above such one-sided interpretations of life. 
If we grasp the principle of this, we have the key to under- 
standing ethical evolution generally, in the individual and 
in the race, and indeed are able to interpret much of life and 
history which is otherwise confusing.! 

Let us take yet another case of inference. What can we 
infer from the following passage? 

"The man ex veritate in the first place understands (with an 
understanding which is at the same time a living in the ful- 
ness of feeling) that the goods of this world are not true 
goods, and would not be unmixed with evil even if we could 
have them all. Pleasure, health, power, consideration, even 
the sweetest affection so far as it is fixed upon a creature who 
will one day vanish like ourselves — all is vanity. Even the 
inward peace, which is the reward of conduct praiseworthy 
from a human standpoint, is illusory and fundamentally sad. 
A life spent in the pursuit of such experiences would not be 
worth living. 

"In the second place he understands (and feels) that person- 
ality, his own as well as that of others, has an intrinsic value. 
Our doing, our suffering, our aspiring after something better, 
must be justified. They are not vain appearances, but reality. 
Whether they take place or do not take place, cannot be all 
one — cannot be indeterminate and inconclusive. Our sight is 
darkened, our desires are disordered and impure, because 
all (or nearly all) of us miss the road. But the true road 
exists. "2 

We can, by processes of inference, construct at least three 
diverse theories of life. (1) From the first paragraph, by 
negating the negations of the ex veritate man, we can obtain 
a positive theoiy w T hich asserts that the goods of this world 
are the only true goods, and that a life spent in the pursuit of 
pleasure, wealth, power, love, and a good conscience, is funda- 

1 The above principle comes from Kegel. 

2 From B. Varisco, The Great Problem^; 1914. 



162 CONSTRUCTIVENESS OF INFERENCE 

mentally joyous and the only life worth living — in short, 
the theory of materialistic optimism. (2) From the second 
paragraph, by proceeding in a similar way, we can construct 
a view of life which asserts that personality is valueless, that 
the pursuit of one end rather than another, and in a word, 
aspiration, effort, and hope, are without significance. For- 
ward or back — it's all one. Upward or down — it's just the 
same. Life is meaningless illusion, and there is no "true 
road. ,, This view we might call materialistic pessimism. 
We can further (la) by negating the pessimistic statements 
at the materialistic level, obtain additional statements of an 
optimistic kind, such as that aspiration and effort, so far as 
productive of pleasure, power, etc., are not illusory, but "real- 
ity," and that a personality developed in the pursuit of such 
aims has a very genuine value. So too (2a), by negating the 
optimistic statements, we can obtain additions to our con- 
struction of the pessimistic view — such as that pleasure, 
health, love, etc., are thoroughly transitory and illusory, and 
that a life spent in pursuing such aims — indeed any life — is 
not worth living. 

On the other hand, (3), by negating the optimist and pessi- 
mist view both, from a standpoint which is not materialistic 
but spiritual, we can construct a positive statement of the 
ex veritate view. For the ex veritate man, it is only so far 
as lived at the materialistic level, that life is not worth while. 
But if our eyes are fixed upon higher aims, if we live our 
life in an idealistic spirit, then pleasure, health, love, con- 
science, etc., take on a new significance. They are no longer 
evanescent and transitory, but — when taken up into the higher 
life of the spirit — become representative of the eternal 
values. Personality ceases to be the mere organisation of 
animal desires at an animal level, and becomes the reflex 
of Divinity, and in the service of the true values comes to 
realise the value which is properly its own. Such a life 
is life at its deepest and best, and is fundamentally joyous, 
and well worth the living. 

The Problem: (A) How Does Inference Construct? — The 
above examples are typical of the constructiveness of infer- 
ence. It is well known that occasions slight in themselves, 
sometimes entail a vast number of important consequences; 
that from the twinkle of a man's eye, or the tone of his 
voice, a popular novelist can deduce "whole volumes" of 



REQUISITES FOR CONSTRUCTION 163 

information about his character, that from two or three 
facts a historian can reconstruct a whole epoch, that from 
two or three bones a palaeontologist can reconstruct the whole 
animal. This power which we have, to construct the whole 
from its part by means of inference, seems very remarkable, 
and in order to understand it we must endeavor to answer 
these two questions: (a) How does inference construct — 
what are the principles, laws, conditions of such construction? 
and (b) How far is inferential construction valid? 

The first requisite of construction is to have the materials 
in such form that they can be put together. That is to say, 
construction pre-supposes analysis. The material must have 
been separated out into elements which can be used in a new 
construction. For geometrical constructions the straight line, 
and some form of conic section, such as the circle, are indis- 
pensable pre-requisites. For the solution of many a problem 
in physics the a, d, c, x% and y^ of algebra are conditions 
without which nothing could be accomplished. For psycho- 
analysis, prepared and standarised association-experiments 
constitute the units. For the diagnosis of mental ability, 
standardised intelligence-tests furnish the material. And 
speaking generally, some kind of unit or element, the prod- 
uct of a preliminary analysis, is the very first requisite for 
inferential construction. 

Elements alone, however, are not sufficient. From straight 
lines and circles we might construct triangles, squares, penta- 
gons, polygons regular and irregular, etc., ad infinitum. From 
the units furnished by the grammatical analysis of a lan- 
guage, we might construct a dissertation in prose or verse 
in -the language in question, or we might construct a gram- 
mar of the language. From algebraic units, we might build 
up solutions of purely theoretical problems, or we might 
solve practical questions in almost any of the applied 
sciences. From the units revealed by psycho-analysis, we 
might proceed to cure a hysterical person by reconstructing 
his dissociated personality^ or we might use the material as 
evidence in support or refutation of some cherished psycho- 
logical hypothesis. From elements alone, anything or nothing 
might be constructed. 

A second requisite of construction, then, is the presence 
of some aim or purpose, some ideal to be realised. If we 

3 Cf. Morton Prince, The Dissociation of a Personality. 



164 CONSTRUCTIVENESS OF INFERENCE 

seat ourselves at the organ, and allow our fingers to wander 
aimlessly over the keys, we are not likely to strike a "grand 
amen," or indeed to produce anything which could be dignified 
by the name of music, any more than the machine described 
by Gulliver after his visit to Laputa was likely to create litera- 
ture of a permanently valuable character.4 It may be true 
that our aims become realised by a process of trial and error 
which is largely governed by chance,^ and our constructions 
so far resemble the Laputan machine. But even so, the pres- 
ence of a definite aim is necessary, at least in order that we 
may know whether our trial was an error or a success. If 
we attend courses at a university with the aim of taking a 
degree, we are far more likely to attain a degree than if our 
attendance is without aim or definite purpose. If we endeavor 
to solve a definite problem in simultaneous quadratics, we are 
far more likely to succeed than if we are just amusing our- 
selves with putting together x% and y%, a and Z), etc. A second 
requisite, then, of constructive inference, is the presence of a 
definite aim or purpose. 

Even this is not quite sufficient. It is not enough to have 
(1) a number of elements and (2) an aim of some sort, or 
even of the same sort as the elements. It is not any and 
every one who can put together the disjecta membra and 
make them into poetry. For that, it takes a poet, one who 
understands the spirit of poetry. So too, in order to build 
a cathedral, something more than good intentions plus the 
materials is essential, namely, a knowledge of architecture at 
least. So too, in order to play Beethoven's sonatas, something 
more is necessary than a knowledge of the position of the 
notes on the instrument, plus an ambition to play the works 
of the Master. Long practise and the gradual building up 
of a technique is essential, as is also an understanding of 
musical problems and of the sonata-form. So too, in order to 
re-construct a historical epoch, something more is necessary 
than the desire to do so, plus certain archeological and literary 
remains — viz., the historian's familiarity with the principles 
of historical construction, both in general, and in connection 
with that special period. 

What is this tertium quid which seems to be necessary? 
The technique of the poet or musician, the understanding 
of the architect or historian — what have these in common? 

4 Gulliver's Travels, Voyage to Laputa, chapter v. 

5 Of. W, B, Pillsbury, Fundamentals of Psychology, pp. 501 ff. 



VALIDITY OF CONSTRUCTION 165 

At least this: familiarity with the means of connecting up 
materials and ideal, a grasp of the schemata and principles of 
construction applicable in these particular fields, an under- 
standing of the structure of poetical or historical composi- 
tion, an apprehension of the nature of the system in question. 
A botanist and a poet observe, let us say, the same aim — e. g., 
a field of poppies. They have, let us say, the same aim — e. g., 
to describe the nature of those poppies. But the scientist 
describes their nature with reference to the systematic study 
of plants. For him they are "phanerogams" with certain medic- 
inal properties. For the poet, on the other hand, they are 
are a vehicle for expressing his deepest emotions and aspira- 
tions. They are symbolic of the laughter and tears, the grief 
and joys of life. The third requisite of construction, then, 
is a grasp of some system — scientific, artistic, or what not — 
in which we can put together the elements which we have 
analysed out, and can build them nearer to the heart's desire, 
shape them into some semblance of our ideal. Given an 
understanding of the principles of systematic construction in 
our particular field, plus elements appropriate for use in 
such construction, plus an aim which is realisable with such 
elements and by such methods, we need nothing further. We 
can proceed to construct our inferences. 

(B) Validity of Inferential Construction. — Not every system 
constructed by inference in all we could wish. All inferential 
construction is hypothetical, and there are many possible 
systems, many rival hypotheses. We are even advised, as a 
point in scientific method, to keep in view, throughout our 
research, a number of alternative possible explanations, so as 
to avoid narrowness. But valuable as is the "method of multi- 
ple working hypotheses" from a practical viewpoint, we can- 
not suppose that, in strict theory, all the hypotheses sug- 
gested are equally true. Some of them are mutually exclu- 
sive^ — in which case, one at least must be false. How are we 
to choose between rival hypotheses? How can we discover 
which of the conceivable systematic constructions is the best? 

Do plants whose leaves are particularly sensitive to light 
have an organ analogous to the primitive eyes found in some 
parts of the animal system? — Or must we seek some other 
hypothesis? Is the three-color hypothesis, or the four-color 
theory to be accepted as an explanation of the facts of human 
color-vision? Is Locke a critical idealist, or is he an empiri- 



166 CONSTRUCTIVENESS OF INFERENCE 

cist with leanings towards realism? Are Plato's "Ideas" to be 
regarded as Super-things, or merely as scientific methods? In 
every field of research this problem is pressing. Is there 
any method or criterion which will enable us to choose with 
certainty between rival explanatory constructions? 

There is no royal road to such knowledge, no short cut 
across the devious, trial-and-error methods of experimental 
inquiry. Progress in knowledge can alone decide, progress in 
verifying or in refuting some suggested hypothesis by strict 
and careful reference to the data. What hypothesis is the 
best, can, in the end, only be discovered, not by some system 
introduced ab extra, but from a study of the system which is 
already present in the data, at least in germ. But to find 
out what system actually is present in the data is often a 
matter of prolonged experimentation with results which 
obstinately remain doubtful. And it is only very gradually 
and tentatively that a rival hypothesis can be eliminated, and 
a more correct one established. 

What is the system, or what are the systems, according 
to which animal cells multiply? Could we think this out? 
We might imagine that the cell would grow by taking in nutri- 
tion, until the tension of its increasing bulk became too strong 
for the containing membranes, and it broke, aided by the 
pressure of external forces — such as the beating of waves in 
the case of water-animals — into two or more cells, each small 
enough to maintain itself in relative equilibrium over against 
the forces of the environment. Beyond this, perhaps, one 
could hardly go a priori. The functions, however, of nucleus 
and nucleolus, of centrosome and chromosome, and in a word 
of all the finer and more intricate elements which play their 
part in the division of cells, could never have been discovered 
in this way. Observation and patient experimenting alone 
could have discovered the system which is the system of the 
data. 

It is necessary, then, to obtain insight into the appropriate 
system — the particular system to which the data, in some 
sense, already belong — if we wish to construct a system which 
will be valid. Given a curve to be completed, it makes a 
serious difference whether we try to complete it by construct- 
ing the form of a circle, of an ellipse, or of a parabola. The 
evidence, however, which is to guide our choice, is to be dis- 
covered only by a careful analysis of the data, e. g., of the 



CONCLUSION 167 

curve in question. So too the principles which are to guide 
our reconstruction of the thought of Plato or of Locke, must 
be sought, not in a study, e. g., of Neokantian philosophy, but 
in a careful study of Plato himself, or of Locke himself. In 
the last analysis, it is there, if anywhere, that the Platonic 
system or the Lockian system will be discovered. Any other 
studies, however, ingenious and however erudite, can lead only 
to unverified hypotheses. 

Conclusion. — Our general conclusion is that from elements 
which are either given, or discovered by analysis, in a concrete 
situation, inference constructs a system which either puts 
together the elements from a new viewpoint, or carries further 
a system which is already present in a fragmentary or partial 
form in the elements themselves. Choice between the different 
possible systems, or in general the validity of inferential 
construction, can be determined only by strict analysis of 
the concrete situation, leading to the discovery of a system 
which is already, to some extent at least, present or implicit 
in the data, and then using this system, and this system only, 
as a principle of construction. 

FOR FURTHER READING 

B. Bosanquet, Logic, Vol. II, pp. 36-42. F. H. Bradley, Principles 
of Logic, pp. 412-414, 419-429. 

EXERCISES 

1. Construct from the following passage a theory of good and 
evil. When you have constructed the theory, point out (1) how you 
have proceeded, and (2) how far your result may reasonably be 
regarded as valid : 

"We are asking whether goods and evils arid obligations exist in 
physical facts per se. Surely there is no status for good and evil to 
exist in, in a purely insentient world. How can one physical fact, 
considered simply as a physical fact, be 'better' than another? Bet- 
terness is not a physical relation. In its mere material capacity, a 
thing can no more be good or bad than it can be pleasant or painful. 
Good for what? Good for the production of another physical fact, 
do you say? But what in a purely physical universe demands the 
production of that other fact? Physical facts simply are or are not; 
and neither when present or absent, can they be supposed to make 
demands. If they do, they can only do so by having desires ; and 
then they 'have ceased to be purely physical facts, and have become 
facts of conscious sensibility." (James, Will to Believe, etc., p. 190). 

2. Construct from the following passage a theory of the habitual 
work of thought. Then point out (1) how you have proceeded, and 
(2) how far your result may reasonably be regarded as valid : 

"Our intelligence can place itself within the mobile reality, and 



168 CONSTRUCTIVENESS OF INFERENCE 

adopt its ceaselessly changing direction — can grasp it by means of 
that intellectual sympathy which we call intuition. This is difficult. 
The mind has to do violence to itself, has to reverse the direction 
of the operation by which it habitually thinks, has perpetually to 
revise, or rather to recast, all its categories. But in this way it will 
attain to fluid concepts, capable of following reality in all its sinuosi- 
ties and of adopting the very movement of the inward life of things. 
To philosophise is thus to invert the habitual direction of the work 
of thought.'* (Bergson, Introduction to Metaphysics, trans. Hulme, 
pp. 69-70). 

3. Construct from the following passage, (1) a theory of the way 
of philosophy, (2) a theory of the way of life, and then point out 
(a) the nature of your procedure in each case, (b) the reasons for 
which your result may be regarded as valid : 

"This I take to be the way of philosophy, of any philosophy which 
seeks to be consistent. It is not the way of life or of common knowl- 
edge, and to commit oneself to such a principle may be said to depend 
upoa choice. The way of life starts from, and in the end it rests 
on, dependence upon feeling, upon that which in the end cannot be 
stated intelligibly. And the way of any understanding of the world 
short of philosophy still rests on this basis. Such understanding 
may despise feeling, and may claim to have risen into a higher region, 
but in the end it will be inconsistent and be found to stand on that 
which, taken as truth, does not satisfy. Outside of philosophy there 
is no consistent course but to accept the unintelligible, and to use 
in its service whatever ideas seem, however inconsistently, to work 
best. The man who stands on particular feeling must remain outside 
of philosophy. If you are willing to be inconsistent, you can never 
be refuted, and that is why philosophy can be said to depend upon 
choice." (Bradley, Essays on Truth and Reality, p. 235). 



CHAPTER XVI 
THEORY OP INFERENCE (1) 

The Problem. — So far we have seen that inference has the 
four main characteristics of dependence, analytical expansion, 
novelty, and systematic constructiveness. The relation of 
these characteristics to one another appears to be somewhat 
as follows: First we analyse down to elements which exhibit 
a certain inter-dependence or law. Then we proceed, in 
accordance with this law of inter-dependence, to construct a 
system which either makes explicit the inter-relation of the 
elements discovered by the analysis, or carries further and 
completes the system of which these elements already consti- 
tute a fragment — as a given curve may be completed in the 
form of a circle or parabola. In this way, whether, by carry- 
ing the system further, we construct something new, or 
whether, by our mere analysis, we discover elements present 
but hitherto unnoticed, inference leads to discovery, to novelty, 
and inference may accordingly be defined as the discovery of 
knowledge by constructing a system based upon analysis of 
a given concrete situation. 

The problem of the present and succeeding chapters is to 
construct a "theory" of inference comparable to our theory of 
judgment, to re-state our present findings in terms of the 
sensory and intellectual factors in our thought, and in short 
to supply an answer to two questions — (1) the question of 
fact, the question of the part actually played in inference by 
sensory and intellectual factors, and (2) the question of 
validity, the question of the reliability and satisfactoriness 
of inference, Tn the present chapter we shall deal with the 
first of these questions. 

The Sensory Elements, (A) In Dependence. — Let us first 
of all consider the more empirical instances. "If the ground 
is wet, the corn will rot." "If I do not hurry, I shall miss 
my car." Is any part played here by sensory, as opposed to 
intellectual, factors? Let us see. The instances appear to 
be analogous to what we called "judgments of experience" in 

169 



170 THEORY OF INFERENCE 

an earlier chapter. Such cases are all generalisations from 
experience, and from an experience which has been largely 
sensory. The wetness of the ground, and so far as that goes, 
the earthmess, the ground-ness of the ground, are matters of 
sensory experience. So too with the appearance of the corn. 
The discoloration, softness, etc., produced by the rot are all 
largely matters of seeing with the eye, testing with the touch 
of the finger, etc. The question of causation is usually 
regarded as intellectual — we do not see what it is that causes 
the rot, but infer or reason. Still, if we were right in attri- 
buting a certain continuity to our sensory experience, the 
gradual change from the firm yellow corn-seed to a mushy 
discolored lump of pulp might be regarded as sensory, pro- 
vided that we abstract from all attempts to account for or 
explain the changes in question. That is to say, the mere 
apprehension of the mushiness at each stage of the degenera- 
tion of the seed can be regarded as a matter of sense-experi- 
ence. But, it may be asked, does sensory apprehension of 
this kind really touch the question of "dependence" at all? 
Our answer must be, No, or at any rate not directly. The 
dependence of rot upon damp cannot be claimed as a matter 
of direct sensory experience. The nearest we can come to 
this is in the continuous apprehension of degeneration in the 
damp medium. This may be regarded as a sensory correlate 
of causal explanation, but in general, it is in apprehending 
the facts to be explained, in taking in the wetness of the 
soil and the mushiness of the seeds, though without putting 
two and two together and drawing a conclusion, that sensory 
apprehension plays a part here. So too sensation assures me 
of my hurrying or not hurrying, of the car standing still and 
of my reaching it, or of the car moving and of my remaining 
upon the spot. But the connection of these facts, the depend- 
ence of my reaching the car upon my hurrying, in a word, 
apprehension of the relation between these two elements, 
seems to be a matter of intellectual, rather than of sensory 
experience. Thus we see that, in both cases, the role of sensa- 
tion seems to be to furnish us with a concrete situation, with 
facts, material, or data, but not in any sense with explanation, 
with apprehension of relations of dependence, whether logical 
or causal. The "hypothetical" element, as such, is non-sensory. 
There is no "If . . . then" about sensation. All that 



SENSORY ELEMENTS 171 

sense-experience can do in such cases, then, is to supply us 
with the materials for inference, with a concrete situation. 

What are we to say about the less empirical cases, e. g. t 
about mathematical dependencies? The equilaterality of a 
triangle is logically connected with its equiangularity, so that 
there is a relation of interdependence. Does sense-perception 
play any part here, or is this, perhaps, a case of "pure" rea- 
soning, of reasoning, that is to say, unmixed with anything 
sensory? So too, in such a case as %2+y2 = 40, if we already 
know that y = 6, we know with mathematical certainty that 
x = 2. That is to say, the conclusion x = 2 is dependent upon 
the two premises. Does sense-perception play any assignable 
part here? Or are we to accept the theory that mathematics 
is the creation of pure thought? There is no doubt that, what- 
ever role sense-perception may play in such cases, it will be, 
at best, a very subordinate one. In the case of geometry, we 
may point to the fact that, while all our geometrical reason- 
ing is general, and is concerned with any triangle and not 
with this particular triangle, still we do not seem able to 
proceed without a figure of some sort. Such a figure has 
definitely sensuous characteristics. If drawn on the board, it 
is white and chalky; if drawn on paper, it is black and inky; 
if drawn in the imagination, it is vague and wavering in out- 
line.- In any case, as apprehended by sense or in sensuous 
imagination, it is concrete, connected with a definite back- 
ground, and contains a thousand other characteristics which 
are equally irrelevant to the strictly intellectual grasp of the 
dependence in question. So too in the case of algebra or 
arithmetic, the #2 and y%, the 1, 2, 3, etc., are represented on 
the paper or in the sensuous imagination by visible symbols 
without which we do not appear able to proceed, and here 
also sensation supplies our thought with a sensory context 
which is largely irrelevant to the mathematical law in ques- 
tion. From a consideration of such cases we come to realise 
that, while inadequate as a representative of mathematical 
laws, sensation does play a part in steadying the attention, in 
giving the intellect a point d'appui for its various operations, 
in short, in providing us with a concrete situation. 

In summary, then, we can state that, if the more empirical 
cases resemble "judgments of experience," the less empirical 
cases resemble what we have called "symbolic judgments," 
and in both cases we see that sensation plays a part without 



172 THEORY OF INFERENCE 

which no inference would be possible. For it supplies us with 
data, with a concrete situation on the basis of which we can 
proceed to reason. This function of sensation is not hypothet- 
ical, but categorical. All explanation or hypothesis, all rising 
above the datum to a grasp of principle, of a law of depend- 
ence, belongs to factors other than sensory. But the situation 
above which we rise and whose law we come to grasp is 
actually present, and we are assured of it by sensation. Of 
this there can be no question. It is categorical. 

(B) In Analytical Expansion. — When faced with a given 
situation, inference does not, like intuition, regard it as a 
totality, as something to be accepted or rejected in toto, but 
proceeds to take it apart, to break it up into smaller factors, 
and generally to reduce it to its constituent elements, so that 
what is relevant can be picked out from what is irrelevant, and 
elements which have passed unnoted in the unanalysed datum 
may one by one be brought under the mental microscope of our 
attention, and nothing may escape. In this process, what part, 
if any, is taken by sense-experience? That it furnishes us with 
the situation from which we start, we have already seen. 
Does it, however, do more than this, and enter in some way 
into the analytical process itself? 

In a way, yes. If, during the process of analysing, we come 
upon some element which has passed unnoted in the totality, 
we apprehend it in a way which is at least in part sensory. 
In fact, each and every element discovered by our analysis, 
whether previously noted or not, is now, at any rate, appre- 
hended in a manner which we can consider as sensory. Sensa- 
tion, then, accompanies every step of our analysis, and accom- 
panies it pari passu. But should we, on this account, regard 
sensation as itself exercising the function of analysis? 

Further consideration will convince us that the presence of 
sensory apprehension, in the final as well as in the earlier 
stages of analysis, is simply the presence of the datum, of the 
concrete situation itself. Analysis cannot go beyond its 
material, but must remain in closest contact with what it is 
analysing, and must guide its every step forward by refer- 
ence to what has been given to it. Hence the presence of 
sensory elements at each step of the analysis. Sensation 
enters into our analysing in no sense other than that in 
which the given situation itself enters in — which is, as a guid- 
ing and controlling influence, at once the material and the 



SENSORY ELEMENTS 173 

ne plus ultra of the process. The sensory factor, then, is 
strictly not analytical, but rather intuitive, accepting what 
is given as a whole, and controlling the process of analysis by 
providing something upon which factors other than sensory 
may exercise their functions — a complex concrete situation. 

(C) In Novelty. — Inference is not content with analysing 
a given situation. It stoops to analysis in order to make dis- 
coveries, to progress, to conquer for knowledge something 
which is new. In this respect it resembles the symbolic judg- 
ment, which, from data drawn largely from actual experience, 
makes judgments which are valid beyond the field of actual 
experience and hold good for possible experience. In such 
cases, cases in which inference leads to the discovery of some- 
thing new, what part, if any, is played by sensation? 

There are, as we saw above, two classes of cases: (1) 
where the novelty, the new information in question, is more 
of the sensory type, and (2) where the new discovery is more 
confined to a special field, the field of relations, which we 
decided to belong more properly to the intellect. In the first 
case — e. g., where, by dipping red and blue litmus paper into 
a liquid and by seeing the blue paper turn red, we infer that 
we have before us an acid and not an alkali, the novelty is of 
the sensory type. As such, it is strictly analogous to the 
case in which analysis reveals the presence of sense-perceiv- 
able characteristics hitherto unnoticed, and the novelty con- 
sists in our now noticing it. That is to say, the function of 
sense-perception in such cases is merely to give us the con- 
crete situation in its full concreteness. The inference, how- 
ever, by which we conclude that the liquid is therefore an acid, 
goes beyond sense-perception and belongs rather to the field 
of relations — in this case, of causal relations. 

In the second case, in which the new discovery belongs 
more especially to the field of relations, as where we make 
discoveries in geometry, or where a person born blind studies 
physical and psychological optics, sensation plays a very sub- 
ordinate role. But in some form it seems always to be pres- 
ent. The figure appears to be necessary in geometrical dis- 
coveries, and the blind man interprets what he studies by 
substituting for the missing visual sensations tactile or kin- 
aesthetic sensations, so far as this is possible — much as we 
try to understand the functioning of the statocyst in Medusa, 
or of the facetted eye in insects, symbolically, as translated 



174 THEORY OF INFERENCE 

into sensory terms which we can connect up with our actual 
experience. 

In both cases the function of the sensory element appears to 
be to steady attention by concentrating it upon a particular 
field. i This special field, within which we proceed to dis- 
cover relations, is the concrete situation from which we start. 
In the case of novelty, then, as well as in the preceding 
cases, while the novelty as such is discovered by factors other 
than sensory, the function of sensation appears to be, to fur- 
nish us with the concrete situation from which we start, and 
by manipulating which we somehow advance to new discov- 
eries. In itself, however, sensation is not progressive or 
novelty-seeking, but accepts passively and conservatively the 
given situation. 

(D) In Systematic Constructiveness. — Discoveries are made 
either by our reorganising the material in such a manner 
that we come to see something which had escaped our notice, 
whether a sensory element or a relation, or else by carrying 
further some system which is already present in the data. 
Given a curve, a few simple geometrical experiments at con- 
struction will inform us whether it is part of a circle, an 
ellipse, or a parabola. Given an examination paper written 
by a student in logic, it is possible to form a fair estimate of 
that student's mental ability so far as logic and kindred 
studies are concerned. Given a few experiments upon memory, 
we can, by constructing a graph from our data, come upon 
striking and suggestive ideas for remembering what we are 
studying. In such cases, what part is played by factors which 
could be called sensory? 

There appear to be two ways in which such factors come 
into play. On the one hand, just as in the preceding cases, 
sensation furnishes us with the concrete situation from which 
we start. The given curve, the examination paper, the results 
of the memory experiments — in apprehending all of these, a 
part is played by sensation, and so far, the function of sensory 
factors resembles precisely their function in the cases we 
have considered. But on the other hand, it seems to do some- 
thing more. Let us examine an instance. Let ABC be any 
given curve. We proceed to test it, to experiment in order to 
see if it is a circle. We draw two chords, AB, BC, and bisect 

i Cf. G. F. Stout, Analytic Psychology, 1896. Bk. II, chapter ii. 



SENSORY ELEMENTS 175 

each chord at right angles. The two bisecting lines meet in 
D. With D as center, and with a radius extending from D 
to B or C, we describe a circle BCE. If the point E coin- 
cides with the point A, so that the curve ABC coincides 
with a portion of the figure BCE, we conclude that the given 
curve is an arc of a circle. But if E and A do not 
coincide, we conclude that the given curve must constitute a 
part of some other figure. Either it is a portion of an ellipse, 
or of a parabola, or perhaps it is altogether irregular. We 
proceed to test each of these hypotheses in a similar way, 
until we come upon one which seems to fulfil all the con- 
ditions. At each step of the construction, sense-perception 
is present. We see the chords AB, BC. We see each step of 
the construction by which they are bisected. We see the 
bisecting lines meet in D. We measure out the radius with 
the aid of sense-perception. We see the curve extended so 
as to form a circle, or so as not to coincide with our circle, as 
the case may be. At every point of our construction, an 
appeal to sensory factors is inevitable. 




In the process of analysis considered above, we noted 
that sense-perception accompanied every step of the process. 
Are the cases of analysis and construction perhaps similar? 
In the case of analysis we saw that the sense-perception in 
question was in fact another name for the concrete situation. 
Analysis of the datum revealed elements which were there, 
but had not been noticed. In the present case, however, 
there is a difference. No analysis as such could extend or pro- 



176 THEORY OF INFERENCE 

duce a curve, and while in some sense we might say that 
extension or legitimate production of a curve is "given" along 
with the curve — for we do not create our extension arbitrarily, 
but construct in accordance with the law of the system which 
is given along with the given portion of that system, viz., 
the curve — still the extension of the curve is not in any 
sense present for sense-perception, awaiting only the direc- 
tion of our attention to it. It cannot be seen before we have 
constructed it. For sense-perception, it is not there. The 
role of sense-perception in construction is thus slightly differ- 
ent from what we found it to be in the case of analysis. And 
yet, in spite of this difference, we feel that in both cases its 
function is to apprehend what is given, and not to add or 
extend, or in any way reconstruct or alter the given situation. 
What, then, are we to say its role is? Does sensory percep- 
tion recognise, perhaps, in some way that the analysis or the 
construction has been carried through correctly? Is it a 
kind of verification of our hypothetical and methodical analy- 
sis or synthesis? Let us consider. All students of mathe- 
matics are familiar with cases in which, owing to some 
slight error in drawing the figure, perhaps accidental and 
unnoticed, a proof will end with the conclusion that a certain 
angle is both equal to, and greater than, a right angle, or 
that two straight lines are both parallel and not parallel, 
t. e., are parallel, and yet meet when produced. In all such 
cases sensuous perception plays precisely the same role as 
when the figure is drawn correctly. By its aid we follow 
each step of the process, and notice that, e. g., A does or 
does not coincide with E. But whether it does or does not 
so coincide, is not usually taken to be a matter of sensuous 
perception as such. No mathematician would dream of rest- 
ing any portion of his proof upon an empirical and varying 
sensory observation. The appeal is always, not to sensation 
qua sensation, but to what is called "mathematical intuition," 
by which we realise, e. g., that two straight lines as such 
cannot enclose a space, that two plus two as such add up to 
four, etc. There is no as such-ness about perception so far as 
it is merely sensuous.2 Verification, then, is the function of 

2 Mathematics is not empirical in the same sense as e. g., my belief 
that the sun is shining. It is not a matter of direct .sensory percep- 
tion. The difference is the difference between empirische and reine 
Anschauung, or between the constdtation empirique and the constata- 
tion logique of a logician like M. Goblot. (Cf. E. Goblot, Traite de 
Logique, 1918, sect. 40). 



INTELLECTUAL FACTORS 177 

factors other than sensory, and the function of sensation 
appears to be rather as an accompaniment, a sine qua non, of 
the process of construction. We could not do without a figure 
of some sort, and the function of sensation appears to be 
to steady the attention and concentrate it upon the features 
of the concrete situation which are to be utilised in guiding 
and controlling the non-sensuous process of systematic con- 
struction. In itself, however, sensation is not constructive, 
but simply accepts without question the concrete situation 
which is given to it, whether this is given as a starting-point, 
or as a result of construction. 

The Intellectual Factors: (A) In Dependence. — "If A, then 
B; if not A, then not B; if B, then A; and if not B, then 
not A." The cases thus symbolised represent what the intel- 
lect demands as the four phases of a genuine depend- 
ence. Taken together, they constitute a system, a mutually 
supporting group of intellectual demands or standards with 
which we approach the empirical data in our attempts at 
inference, at obtaining insight into some law. As such, i. e., 
as constituting a systematic group or organisation, they are 
subject to the standards which govern such groupings, that 
is to say, the standards of identity, difference, and organisa- 
tion, internal and external. On its intellectual side, our 
thought directs its attention exclusively to those features of 
the concrete situation which are relevant to this point of 
view, and the result of the application of such standards is 
always to leave us with a mere skeleton of the concrete situa- 
tion with which we started out, an abstract system of rela- 
tions which satisfies the intellectual demand so far as it can 
be satisfied w.thout going illegitimately beyond the given 
material. The details of this have been already sufficiently 
considered in our study of the application of intellectual 
standards in the case, for instance, of the symbolic judgment. 
The only significant difference is that here, instead of stand- 
ards of organisation in general, and of consistency within a 
system in general, we have a very definite system with four 
main aspects, the system of logical dependence. 

(B) In Analytical Expansion. — Analysis is a peculiarly 
intellectual function, and especially involves the standards 
of identity and difference. The concrete situation is envis- 
aged as a complex, and this complex is taken apart and 
resolved into its constituent elements, one after another, For 



178 THEORY OF INFERENCE 

example, I have applied for a position, and am using what 
powers of inference I possess, in order to discover if I can, 
what my chances are. The concrete situation from which I 
start is, in this case, all the information of whatever kind I 
have which in any way bears upon the subject. It is, how- 
ever, not clear to me, but is hopelessly entangled in a mass of 
prejudices, hopes, and fears, which effectually interfere with 
my intellectual vision. By making use of the standard of 
identity, I run over this mass of material with a single idea 
in mind, and select every element which in any way bears 
upon, e. g., my own merits, taking these one by one. By 
means of the standard of difference, I reject everything which 
does not bear upon each particular point, as associations 
bring up fresh material, and by using both standards in this 
way in clearing up one point after another, I at last have 
the whole of the irrelevant material separated off, and the 
whole of the relevant material carefully sorted out, so that I 
can proceed to weigh the evidence scientifically, with as full 
knowledge as possible and without undue bias from emotion 
or from the confusing mass of the material. 

Let us examine another case, of a different kind. Take the 
following passage: 3 

"This good, then, which every soul pursues, as the end of 
all its actions, divining its existence, but perplexed and unable 
to apprehend satisfactorily its nature, or to enjoy that steady 
confidence in relation to it, which it does enjoy in relation to 
other things, and therefore doomed to forfeit any advantage 
which it might have derived from those same things; — are we 
to maintain that, on a subject of such overwhelming impor- 
tance, the blindness we have described is a desirable feature in 
the character of those best members of the state in whose 
hands everything is to be placed?" 

This passage constitutes a single sentence. But it is so dif- 
ficult that without analytical inference we can hardly hope 
to understand it. Let us analyse it, using the standards of 
identity and difference so as to take one thing at a time. 
Suppose we take first our own predicament — the predicament 
in which "every soul" finds itself. We are pursuing some 
good as the goal of our every action. We intuitively believe 
in the existence of this goal towards which we are working, 

3 Plato's Republic, Bk. VI, pp. 505 E to 506 A. (Trans. Davies 
and Vaughan). 



INTELLECTUAL FACTORS 179 

but are unable to apprehend its nature. We are perplexed, 
and do not know what the goal actually is. In other cases, 
(e. g., money, pleasure, learning, peace of mind), where we 
know what these are and understand their nature, we are 
not perplexed, but enjoy a steady confidence in regard to 
them. But in the case of this goal towards which we believe 
ourselves to be working — not exactly knowing what it is, we 
are without confidence, and do not know where we stand. 
Further, not knowing what the goal of life is, we do not 
know how we should arrange our life in respect to these 
other things (money, etc.,) — we do not know how to select 
wisely, and therefore cannot make the most of them. Is 
ignorance of the goal of life, from which it derives its whole 
meaning — is ignorance in a matter so fundamental, desirable? 
If it is not desirable in our own case, is it not still less 
so in the case of the rulers of the State? If our great men 
also are blind, will not the blind be leading the blind ?4 

From this instance we see that taking a single view-point 
and omitting everything which is irrelevant introduces con- 
siderable clearness into our mental grasp of what was there 
to be apprehended. In the same way, by proceeding to make 
''the good" the object of our investigation, or the distinction 
between ''divining the existence of" the end of life and "appre- 
hending the nature of" other things such as money, pleasure, 
etc., and similarly taking up one point after another, we 
could make the meaning of the passage as a whole much 
clearer. In general, we can say that the function of the intel- 
lectual factors in analysis is, while not leaving the starting- 
point or in any way going beyond the information which is 
given to us, so to introduce the standards of identity and 
difference, as to lead up to a carefully arranged articulation 
and classification of all which is relevant, and a strict removal 
of everything vrhich is irrelevant. This sifting out of every 
element to which we attend leads to such an organisation 
of our thought that, in place of confusion and mental chaos, 
we have order and clearness. It may be at times that the 
given situation does not contain enough information to satisfy 
our every question, reorganise it as we may. But after such 
analysis has been completed, we at least know where we 



4 So as not to take up too much space by making two analyses, 
there is included in the above the result of a previous analysis which 
discovered that the good is the goal of life. 



180 THEORY OF INFERENCE 

stand. No item of information has escaped us, and if an 
answer is there to be discovered, methodical analysis is prac- 
tically certain to bring it to light. 

(C) In Novelty. — Inference is not fully satisfied with the 
clearness whicn results from analysis. It is not merely to 
make our thought clear, to purge it of confusion, to see our 
way more plainly, that we infer. We infer so as to discover 
an answer to some question which we cannot possibly answer 
otherwise, to make our way out of some difficulty which is 
otherwise hopeless, to obtain some advantage which other- 
wise we could not obtain. Inference discovers something 
which is new. In such discovery, what part is played by 
factors which could be regarded as intellectual? 

Let us consider. In the above passage from Plato, for 
instance, we did not know, until after our analysis, what 
was meant by the clause "and therefore doomed to blindness 
. " Probably we did not feel sure about what was 
meant by the "blindness" of the statesmen. Our analysis 
thus not only made our thought clear, but made us see our 
way where previously we had been entirely in the dark. In 
this way elements concealed by their context can be discov- 
ered by analysis, and so far "novelty" receives the same 
treatment as "analysis." It is by applying the standards 
of identity and difference with methodical regularity that 
we make discoveries of this character, that we light upon 
something which was already there, awaiting the application 
of precisely such methods. 

There are, however, other cases which are not so simple. 
For instance, most problems worked out by simultaneous 
equations give us information which is new, but which can 
hardly be said to have been present, merely overlaid by an 
irrelevant and confusing context, and thus concealed from 
view. I miss my train, and two hours later take an express 
which follows it at a slightly more rapid rate — e. g., ten miles 
an hour faster. When and where shall I catch up with my 
proper train and make my transfer? There is no doubt that 
an answer to this question in some sense is "given" along 
with the conditions, and that it can, as we say, be "worked 
out" and duly discovered. But there is also no doubt that 
something more is needed than merely taking to pieces the 
data and scrutinising them one by one. By analysis I learn 
that the first train moves at forty miles an hour; that my 



INTELLECTUAL FACTORS 181 

train moves at fifty miles an hour; that the first train is two 
hours ahead; etc., etc. But just when and where the express 
will catch up with it — that I cannot by this method discover. 
It has to be worked out. In such cases a certain extension 
of the intellectual framework of the concrete situation takes 
place, and it is in relation to this extension that the answer is 
worked out and the discovery actually made. But the general 
method does not differ very seriously. I use x and y in 
working out my problem — i. e., mental counters, sharply differ- 
entiated identities — and it is by the substitution, for the con- 
crete situation, of such results of the application of the 
standards of identity and difference, that I am able to solve 
my problem. la the case of novelty, then, as in the preced- 
ing cases, the function of intellect is to apply the standards 
of identity, difference, and organisation so as to substitute an 
intellectualised model which is confined to essentials for the 
concrete reality which contains so much which is irrelevant 
and does not admit of that intellectual manipulation which 
leads to discoveries. 

(D) In Systematic Constructiveness. — Inferential con- 
struction goes beyond mere analysis, but still without chang- 
ing fundamentally the character of its data. In such con- 
struction we produce a straight line, for instance, to twice 
or thrice its given length. It is still, however, a straight 
line. We complete a curve, e. g., by adding the missing por- 
tions of the ellipse of which it constitutes a fragment. The 
curve is still the same curve. On the third side of a given 
triangle we construct a parallelogram equal to the sum of 
any two parallelograms given on the other two sides We 
have not, however, by so doing, altered the nature of the 
given triangle or the given parallelograms. So too we put 
together all we know of the character of Mr. X, and infer 
to his probable course of action in a certain contingency. 
We have not, however, altered the nature of our information 
by so extending it. 

What intellectual factors are involved in such construction? 
In the first place, we use the standard of identity. In 
extending a straight line, we must continue to produce it in 
one and the same direction. In completing the ellipse, we 
must hold fast to the method of constructing the ellipse of 
which the given curve forms a part. In calculating Mr. X's 
probable action, we must follow the identical line of thought 



182 THEORY OF INFERENCE 

established by our previous knowledge. In the second place, 
we use the standard of difference. We refuse to swerve from 
the identical direction of the given line. We refuse to wander 
from the path established by the given portion of the ellipse. 
We decline to allow hopes or prejudices to influence our 
calculation of Mr. X's probable course of action. In the third 
place, we make use of the standards of organisation, internal 
and external, in constructing our system, whether that system 
be simple, as in the case of a straight line or ellipse, or 
complex, as in the case of character-analysis and character- 
construction. That is to say, in constructing systems we 
employ the same intellectual factors which we used in analysis, 
but on a slightly more extended scale — the standards of iden- 
tity, difference, and organisation — and employ them in such 
a way that we start with a concrete situation and end up with 
a mental model, an abstract plan or system which omits many 
of the factors present in the given situation, and now includes 
elements which go beyond the situation with which we 
started, not however by altering its character, but by extend- 
ing it. 

Summary — The Sensory and Intellectual Factors in Infer- 
ence. — In inference, then, the function of sensory factors is 
categorical, intuitive, conservative, receptive. Sense receives 
without question what is given to it, accepts and preserves 
it without alteration, and in a word presents us with the 
material for intellectual operations, a concrete situation which 
forms a starting-point for inference. The function of intellect 
is hypothetical, analytical, novelty-seeking, constructive, 
progressive. It receives nothing without question, works over 
what is given to it, omits here and extends there, re-arranges, 
sifts, and is not satisfied until it has substituted for the given 
material an intellectualised structure from the inter-relation 
of whose parts it obtains an insight which is new, and which 
leads us far beyond the concrete situation which was orig- 
inally given to us. In so doing, however, it attempts to con- 
fine itself to alterations and additions which are legitimate. 
How this is possible, we must now proceed to inquire. 



FOR FURTHER READING 

F. H. Bradley, Principles of Logic, Bk. Ill, Part I, chapter vii. 
J. E. Oreighton, An Introductory Logic, chapter xxiv. J. Royce, 



EXERCISES 183 

Sources of Religious Insight, chapter iii. W. Wundt, Logik, (3rd 
Edit), Vol. I, pp. 296-301. 

EXERCISES 

1. Construct, in systematic form, a statement of the part played 
by personality in the world, according to the following passage. Then 
point out (1) the sensory elements, (2) the intellectual elements, 
used in your procedure : 

"I do not see why the very existence of an invisible world may 
not in part depend on the personal response which any one of us 
may make to the religious appeal. I do not know what the sweat 
and blood and tragedy of this life mean, if they mean anything short 
of this. If this life be not a real fight, in which something is eternally 
gained for the universe by success, it is no better than a game of 
private theatricals from which one may withdraw at will. But it 
feels like a real fight, as if there were something really wild in the 
universe which we. with all our idealities and faithfulnesses, are 
needed to redeem. — For such a half-wild, half saved universe, our 
nature is adapted." (James, Will to Believe, etc., p. 61). 

2. Construct from the following passage, (a) a theory of Truth, 
(b) a theory of Reality. Then point out (1) the sensory, (2) the 
intellectual elements used in your procedure : 

"Reality for me is one in-dividual experience. It is a higher reality 
above our immediate experience, and above all ideality and relations. 
It is above thought and will and aesthetic perception. But, though 
transcending these modes of experience, it includes them all fully. 
Such a whole is Reality, and, as against this whole, truth is merely 
ideal. It is indeed never a mere idea, for certainly there are no 
mere ideas. It is Reality appearing and expressing itself in that 
one-sided way which we call ideal. Hence truth is identical with 
Reality in the sense that, in order to perfect itself, it would have 
to become Reality. On the other side, truth, while it is truth, differs 
from Reality, and, if it ceased to be different, would cease to be true. 
But how in detail all this is possible, cannot be understood. (Bradley, 
Essays on Truth and Reality, pp. 343-344). 



CHAPTER XVII 

THEORY OP INFERENCE (II) 

VALIDITY OF INFERENCE 

The Problem. — So far we have seen what part is, in fact, 
played in inference by factors which are intellectual. Sense 
supplies us with the concrete situation from which we start, 
while intellect operates by taking apart this situation and 
presenting us, in its place, with a mental model which contains 
only factors which we can understand-^a working model 
which we can take to pieces and put together again because 
we apprehend its principle of construction. Our present prob- 
lem is to consider how far this procedure is valid, how far 
inference is reliable, how far a mental model which we can 
take to pieces and put together again represents accurately 
and truthfully the reality with which we wish to make con- 
tact, or to keep in contact. 

In view of our earlier discussion,! it is unnecessary to 
inquire now in what sensory validity and intellectual validity 
respectively consist. In such cases as we have in mind, 
validity is purely a matter of direct sensory apprehension, 
or of direct intellectual apprehension of the results of apply- 
ing strict intellectual standards. If we avoid misleading 
associations, and subject the sensory elements to direct appre- 
hension, this is, as we have seen, ultimate, the last court of 
appeal, and is so far satisfactory. If, again, we have con- 
structed our mental model after strict analysis into intellectu- 
alised elements — sharply differentiated identities which can 
be used as mental counters — and have constructed it in 
accordance with the principles of identity, difference, and 
organisation, then on the intellectual side it is so far satis- 
factory. The only question which remains is the question 
of general validity as opposed to a validity which is specif- 
ically sensory or specifically intellectual. How far is our 

i See chapters Viii and tx. 

184 



DEPENDENCE 185 

intellectual structure satisfactory from a viewpoint which is 
not merely intellectual, but includes sensory aspects also? 
How far is our sensuous apprehension valid from a viewpoint 
which includes also the aspect of intellectual demand? 

Dependence. — As we have seen, the function of sensation 
is to give us our starting-point. Granted that every associa- 
tion which might mislead has failed to do so, granted that 
there is no flaw in the direct apprehension with which we 
see with our eyes the corn-seeds once so yellow become dis- 
colored, and with our finger feel their firmness change to a 
soft pulpiness — is this continuous sensory apprehension all 
we need to assure us of the presence of a law of cause and 
effect? Can we state, on the basis of an apprehension which 
is merely sensuous, however valid it may be, that a continu- 
ous sensory sequence is governed by a law? Can we state 
that the visible discoloration and palpable rottenness is caused 
by the visible and palpable wetness of the soil? 

There can be no doubt that such sensuous observation pro- 
vides us with the evidence by reference to which we verify 
our conclusion. But of itself, an apprehension which is merely 
sensuous can furnish us with nothing which is not itself 
sensory. A law is not something which one can see with 
the eye or handle with the fingers. A hypothesis is not 
directly apprehensible by the organs of taste or smell, and 
consequently, however direct and accurate sensuous appre- 
hension may be, it is always unable to give us direct assur- 
ance, valid or invalid, of dependence, whether causal or logical. 
Sensation supplies us with the material for reasoning, with 
a given situation from which we proceed to infer and draw 
conclusions. But this basis or starting-point being given, the 
inferring or reasoning itself must be accomplished by ele- 
ments other than sensory, and it is accordingly in respect 
of these further elements that we must ask how far inference 
is valid. 

Prom the sensory starting-point described above, and by 
applying the standards of identity, difference, and organisa- 
tion, I come to the conclusion that if the ground is continu- 
ously damp, the seeds become rotten; that if the ground is 
not continuously wet, the seeds develop normally; that if the 
seeds become rotten, the ground must have been unreason- 
ably damp; and finally, that if the seeds develop normally, 
we may be reasonably sure that the ground was not unduly 



186 VALIDITY OF INFERENCE 

moist. That is to say, I infer that there is a causal connec- 
tion between excessive moisture in the environment and 
degeneration of the seeds. On what does the validity of this 
conclusion depend? 

Assuming the mental pattern of cause and effect, why do 
we select this particular cause for this particular effect? 
That is, why do we select from our sensuous experience just 
this one element — excessive dampness of the soil — as the 
factor which counts? Not merely because it is in accordance 
with what we know of the effect of moisture in general, but 
because such a supposition fits in with, and is supported by, 
the sensory evidence in the case in question. It is satisfac- 
tory only so far as experience bears it out. If we could plant 
corn with impunity in the early days of spring, when the 
ground is especially moist, we should not accept the hypoth- 
esis in question. We should say, it sounded well in theory 
but did not work in practice — in other words, that it was 
not verified in sensory experience. But in the long run, 
experience does verify it, and accordingly farmers wait till 
the damp season is over before they plant their corn. 

If, then, we may take this case as typical of relations of 
dependence, we can say that the validity of inference, in this 
field, depends upon our introducing, as a principle of organi- 
sation, a mental pattern which is satisfactory, not merely 
to the intellect with its general desire to understand, but 
also to sensory experience, which presents us with this par- 
ticular situation as a problem to be solved. So far as the 
mental model is not only intelligible but also the pattern in 
accordance with which the concrete situation actually seems 
to behave — so far as we get insight, not merely into artificial, 
intellectual constructions, but also into the workings of the 
concrete situation itself — our inference is valid. 

Analytical Expansion. — Here also sensation furnishes us 
with the concrete situation from which we start, and, of 
itself, sensation is peculiarly unable to analyse. It accepts 
intuitively, as a totality, whatever is given to it. Here also, 
then, the question of validity of inference will be concerned 
mainly in examining the claims of our intellectual operations 
to general validity. Let us take an example: 

"We do not see the actual things themselves; in most cases 
we confine ourselves to reading the labels affixed to them. 
This tendency, the result of need, has become even more pro- 



ANALYTICAL EXPANSION 187 

nounced under the influence of speech; for words — with the 
exception of proper nouns — all denote genera. The word, 
which only takes note of the most ordinary function and com- 
monplace aspect of the thing, intervenes between it and our- 
selves, and would conceal its form from our eyes, were that 
form not already masked beneath the necessities that brought 
the word into existence. Not only external objects, but even 
our own mental states, are screened from us in their inmost, 
their personal aspect, in the original life they possess. When 
we feel love or hatred, when we are gay or sad, is it really 
the feeling itself that reaches our consciousness with those 
innumerable shades of meaning and deep resounding echoes 
that make it altogether our own? . . . Mostly, we per- 
ceive nothing but the outward display of our mental state. 
We catch only the impersonal aspect of our feelings, that 
aspect which speech has set down once for all because it is 
almost the same, in the same conditions, for all men. Thus, 
even in our own individual, individuality escapes our ken. "2 

Let us regard this passage as a given situation and proceed 
to analyse it. We select a single viewpoint, and direct our 
thought into a single channel, taking in from the given situ- 
ation every element which is of significance for this viewpoint, 
and omitting or rejecting everything which is irrelevant. Let 
us take for our first aim, to make a list of everything which 
is stated or clearly implied about "Things." 

Things are other than we see them — are more than the labels 
which are attached to them — have, in addition to the super- 
ficial aspects, aspects which are profound, unusual, unfamiliar 
— aspects of a deeper nature which is beyond naming, and is 
profoundly individual — which, to be apprehended as it is, 
must be regarded from some viewpoint which goes beyond 
merely practical interests, etc. 

So too with our innermost feelings. Like things, these have 
an intrinsic essence, a life and individuality of their own, 
infinitely more profound than the superficial aspects which 
do duty for every-day purposes. If we wish to grasp them 
in their true individuality, we must use some method differ- 
ent from discursive thought, which seizes only upon aspects 
which are general, and can be expressed by names. 

Then again we can take our own "knowledge. We are thor- 

2 After Bergson, Essay on Laughter. 



188 VALIDITY OF INFERENCE 

oughly practical, in science no less than in ordinary life. We 
grasp at the easiest, most superficial aspects of things and of 
our selves, being satisfied with what will work for practical 
purpose. We are driven to do this by the pressure of prac- 
tical necessities, and as an aid to this kind of life have 
invented language — general expressions which come between 
us and ultimate realities, until we have come to live in a 
world of mental fictions, general concepts which we can use 
for scientific purposes, but which conceal from us the vital 
essence of our selves no less than of things. 

So too, we might pay especial attention to language, or to 
individuality, etc., or to the interconnection of these concepts, 
and so make one element in the passage after another the 
subject of a detailed study, until every single element had 
been considered in turn and nothing had been omitted. In 
this way the whole passage would have been analysed and 
expanded. 

Regarding this instance as typical of the work of analysis, 
let us proceed to ask how far such procedure is legitimate. 
The end-point is very different from the starting-point. We 
have taken each element out of its given context, have placed 
together in a new context elements taken from different parts 
of the passage, in such a way that they seem to throw upon 
one another a light which is new. At any rate, the patterns 
according to which the passage has been analysed and the 
results classified together in the above groups, were introduced 
by us in analysing, and it may well be questioned how far 
such interference with contexts is legitimate.3 

That such procedure adds to our insight, is certain. The 
new patterns of arrangement, the taking one point at a time, 
the putting together every item of meaning which refers to 
one and the same point, is undoubtedly helpful in introducing 
clearness and intelligibility into the given passage. The only 
question which rises in our minds is, whether our procedure 
is not, perhaps, after all subjective, a mental luxury which 
makes our-convenience-in-understanding the first thing and is 
unjust to the passage — or whether our analysis has an objec- 
tive significance. There is no doubt that such tampering with 
contexts is sometimes illegitimate. Under the influence of 
political or personal feeling, men analyse each other's utter- 

3 Of. Bradley, Principles of Logic, pp. 499-500. 



ANALYTICAL EXPANSION 189 

ances in a way which makes sufficiently clear to themselves 
how base are the intentions of the other party. But it is 
well known how biased and unreliable such analyses are. 
Analysis, then, may be biased or possibly unbiased, and may 
be reliable, or possibly unreliable. What is to be our crite- 
rion? How are we to know when an analysis is reliable, and 
when it is not? 

The answer is plain. Analysis is to be trusted, when it is 
the analysis of the given situation, when the substitution of 
one context for another makes clearer a meaning which is 
already there, but is not, perhaps, so clearly expressed. Tak- 
ing one point after another is justified, so far as such a 
method makes intelligible the sense of the given passage. If 
it throws light upon the datum, and makes clear the intellectual 
context of the concrete situation itself, any such procedure is 
thoroughly justified. If however the introduction of new 
angles of approach obscures or falsifies — as prejudice, for 
example, obscures and falsifies — it is illegitimate. The veri- 
fication, then, of an analysis involves patient and constant 
reference to the given material — reference at each forward 
step, as well as at the final conclusion, and at the final con- 
clusion as well as at each forward step. Only thus can we be 
certain that the introduction of the intellectual standards of 
identity, difference, and organisation is satisfactory to our sen- 
sory, as well as to our intellectual, apprehension. 

This seems, perhaps, so simple as to be hardly worth 
stating. And yet, everywhere one looks, one finds examples 
of what to avoid. Without the most patient and continuous 
reference to the given situation, the most ingenious and per- 
sistent attempts at analytical expansion serve only to divert 
from the path and to lead to constructions which are built 
upon no reliable foundation. The student who is familiar 
with modern attempts at Shakespearean interpretation is 
well aware that many of the attempts, literary as well as 
psychological, evince the utmost subtlety of analysis, the most 
rigid and patient following out of one path at a time. And 
yet, sometimes half-way through, and almost always at the 
end, the reader of these novel explanations, while forced to 
admire the analytical dexterity and logical or psychological 
acumen of the critic, and the extreme clearness and fascinat- 
ing persuasiveness of his mental patterns, is forced also to 



190 VALIDITY OF INFERENCE 

ask himself — can this possibly be Shakespeare? Only too 
often the answer is in the negative. 

The validity of analytical expansion, then, is determined 
in the last resort, not merely by applying standards which 
satisfy the intellectual demand for clearness and consistency 
of outlook, but also by reference to the concrete situation 
from which we started. Only so far as the meaning which 
our methods succeed in extracting from the material is the 
meaning of the situation itself, is our analysis verifiable and 
accepted as legitimate. 

Novelty.— The persistent application of methodical infer- 
ence usually results in an insight which reveals something 
novel, discovers something new, or at least previously 
unnoticed. By putting two and two together, we discover 
something which otherwise, perhaps, would have escaped our 
most "careful scrutiny — such as the age of a new minister, 
some vexed problem of authorship, or the solution of some 
historical problem, for example, the question as to the pass 
by which Hannibal crossed the Alps. By the careful and 
methodical analysis of a complex situation, we discover some- 
thing which would otherwise have been missed by that super- 
ficial acquaintance which does duty for every-day purposes. 
By the simple extension of something which we already know, 
we may make discoveries of enormous importance for our 
whole future development. To the student who can at last 
read a hundred lines of the Aeneid in an hour, it occurs, with 
something of a mental shock, that he can read two hundred 
lines in two hours, or, further, that since there are only 
between seven and eight hundred lines in the average book, 
he can read a whole book in a single day, or even — illuminat- 
ing and inspiring thought! — the whole Aeneid in less than a 
fortnight. To the student who has been accustomed to spend- 
ing the greater part of a term over a single book, this exten- 
sion of what he already knows comes with all the force of 
novelty, and is the source of a new insight which may alter 
his whole future plans of study, and indeed may affect radi- 
cally his choice of a profession. 

How far is such novelty trustworthy? It is by analysis, by 
extension, or by putting two and two together, that we make 
discoveries of this kind, and it is so far as these methods — 
of analysis, extension, and construction of systems — are valid, 
that their results can be accepted without misgiving. The 



NOVELTY 191 

case of analysis we have already discussed, and at the present 
stage we can say definitely that so far as our intellectual 
operations upon the given material result in unearthing some- 
thing which was already there, present in the concrete situa- 
tion but unnoticed, so far such inferences are sufficiently 
reliable. The case of extension and construction of systems 
will be left for the next section, but at present we can say 
that so far as such extensions are legitimately involved in 
the concrete situation — i. e., so far as they follow reasonably 
upon what is given — they are to be trusted, and, in general, 
our conclusion is that inferences which result in new discov- 
eries are valid so far as they bring to light something which 
was already present, or is logically implied by what is present, 
in the given situation from which we start. 

Constructiveness. — Inference is constructive. If a some- 
what lengthy package is delivered to our neighbor from a 
delivery van with the sign "Sporting Goods," and we see our 
neighbor digging in his garden for worms that evening, any 
reasonable person will reconstruct for himself the scene which 
is to be enacted the following morning, and the part which 
will be played by the contents of the package — even though 
he is without special knowledge of his neighbor. If a psycho- 
analytical examination reveals undue hesitation in reacting 
to the stimulus-words "Ring," "Woman," "Marriage," "Voyage," 
etc., we should draw our own conclusions as to the state of 
mind of the subject, and could reconstruct certain of his chief 
interests and portions of his recent history with fair accu- 
racy, even though we had never seen him before. So too from 
a few scattered notices taken from the works of ancient critics, 
a modern scholar will reconstruct the outlines of a lost play 
by Euripides or Menander, much in the same way as from a 
few bones an anatomist will reconstruct a mammoth or eohip- 
pus, or an anthropologist will reason from the disposition 
of the remains of a pre-historic man that he had a religion 
and believed in the immortality of the soul.4 

What are we to say as to the validity of such inferential 
constructions? They are all, of course, hypothetical, and none 
of them are absolutely certain. But when we thus go beyond 
the immediately present facts and enlarge upon our data, 
regarding them as fragments of some greater hypothetical 

*Cf. R. R. Marett, Anthropology, p. 206. 



192 VALIDITY OF INFERENCE 

system, is our procedure so reliable as to be beyond reasonable 
suspicion? Let us consider what we do in making such con- 
structions. We analyse the concrete situation which is given 
te us, take it apart into its elements, intensify the identity 
and difference aspects of these elements until they can be 
used as mental counters, contextless or almost contextless 
entities which can be put together in accordance with almost 
any intellectual pattern, until we end up with a mental model 
which we can take apart and put together again with fair 
insight into the principle in accordance with which we have 
constructed it. Instead of the concrete situation with which 
we started, we have an almost contextless artefact, intelligible 
indeed, but connected, at best, only remotely with the facts 
of sensory experience with which we started. How far is 
this inferential procedure to be accepted as reliable? 

That such systems are at times far from trustworthy, is 
beyond doubt. From the paranoiac or the adolescent who sees 
everyone in a conspiracy against him, to the optimist who 
sees everything without exception working wholly for his best 
in this best of all possible worlds, the products of intellectual 
construction do not escape a certain suspicion, and even in 
the sphere of scientific research, many a brilliant theory has 
been discarded, as going too far beyond the evidence. N-rays 
whose "faint luminosity" is invisible to everyone except their 
discoverer,^ Phlogiston, the Geo-centric view of astronomy — 
how many doubtful hypotheses have been constructed in the 
tragi-comedy unfolded in the history of culture? What is 
it, then, which makes us trust one construction, and regard 
another system as wholly unreliable? 

Let us consider. In the case of rival hypotheses — different 
and opposed theories to account for the same group of phenom- 
ena — on what basis do we make our choice? For example, 
do plants grow upwards because they love the sun, or because 
they have a special organ analogous to the statocyst in the 
animal kingdom? That is to say, is the explanation of their 
growth to be in terms of a simple, unmediated heliotropism, 
or in terms of a more complex organ for appreciating the influ- 
ence of the earth's gravity? Or, if perhaps both factors are 
present, which plays the greater part? There is only one 
way to find out with reasonable certainty. We must devise 

s Of. Ooblot, Traite de Logique, pp. 49-50. 



THEORY OF INFERENCE 193 

experiments which will bring only one factor — e. g., gravita- 
tion — into play at a time, and see how our test-specimens actu- 
ally behave. We must also dissect a reasonable number of 
plants, and find out whether there is present anatomical evi- 
dence of the complex organs in question. That is to say, we 
can choose between rival hypotheses, or for that matter verify 
a single hypothesis, only by careful study of the concrete 
situation itself, in order to discover whether the suggested 
system is present in, or implied in, the data. If the sug- 
gested explanation is intellectually satisfactory — i. e., if we 
can take the mental model to pieces and put it together again 
with a reasonable degree of insight into the law of its con- 
struction — the only question as to its validity is, whether it 
is or is not a system present in, or implied in, the data. If 
it proves to be the system of the concrete situation, then we 
can regard our reconstruction as an explanation of the data, 
and if it is in accordance with all that is known in that par- 
ticular field, we tend to regard the explanation as to be 
accepted. Validity, then, in the construction of systems, 
depends wholly upon whether the intellectual context which 
we thus construct proves to be the intellectual context of the 
data themselves, or at least a .reasonable extension of such 
context. 

Conclusion — The Theory of Inference. — In this way we come 
to realise that the theory of inference and the theory of judg- 
ment are one and the same. The movement of our thought, 
whether in judgment or in inference, if it is to be regarded as 
valid, must satisfy certain conditions. It starts with a datum, 
a concrete situation with which we are in touch largely by 
means of sense-perception. This datum it analyses and 
remodels until it is shaped more in accord with intellectual 
demands — i. e., until the intelligible elements in the given 
situation which are relevant to our special viewpoint are 
placed in their proper intellectual setting, so that their inter- 
relation can be sufficiently understood. The validity of such 
thought-activities depends wholly on whether the operations 
of sense-perception and of intellectual reconstruction are per- 
formed accurately, not merely in themselves, as taken singly 
and separately, but as taken together, with especial reference 
to each other. Each single step of the process, from the first 
sensory apprehension to the last remodelling in the intellect, 
should be verifiable by explicit reference to the concrete 



194 VALIDITY OF INFERENCE 

datum, and each element of sensuous apprehension should be 
purified from carelessness and misleading associations by a 
critical attitude which ensures as close conformity to intel- 
lectual standards as the nature of the case admits. 

FOR FURTHER READING 

F. H. Bradley, Principles of Logic, Bk. Ill, Part II, chapters iii-iv. 
Chr. Sigwart, Logic, Vol. II, pp. 5-23, 464-480. W. Wundt, Logik, 
(3rd Edit.), Vol. I, pp. 302-308. 

EXERCISES 

On what does the validity of the following inferences depend: (1) 
A sailor, coasting along the shore of an unknown land, one morning 
notices that he is passing scenery which he passed four days before 
— and infers that the unknown land must be an island. (2) Writers 
of almanacs tell us beforehand when eclipses are to take place. This 
ihas been inferred. (3) We leave home in the morning, and infer 
that when we return in the evening our home will still be there. 

4. We place a letter on our private mail box, and after a few hours, 
notice that it is no longer there. We infer that the postman has 
taken it. (5) vVe look out of the window in the morning, and see 
the ground white with frost. We infer that the tomato plants have 
been killed. (6) We read in the paper that Mr. X has been elected 
president, and infer that this statement is true. (7) We look at the 
clock and find that it indicates an absurdly impossible time. We 
infer that we must have forgotten to wind it. (8) We read in the 
paper "Wanted, a man to drive a team with religious views," and 
infer that a comma must have dropped out. (9) We listen to a piece 
of music, and infer that it must have been composed by Beethoven. 
(10) We infer that, if we continue to work hard along the lines 
which interest us, we shall certainly be successful in the end? 



PART III 
SCIENTIFIC METHOD 



195 



CHAPTER XVIII 
GENERAL CHARACTERISTICS OF SCIENTIFIC METHOD 

Unscientific and Scientific Method. — A and B have each a 
business in the same town. A has three clerks, and each 
clerk does what he can. During the busy part of the day, 
every one keeps busy attending to customers, but during the 
slack times, when there is less to do, less is done. ' Each 
clerk knows as much about the business as the others, and 
any one of them is ready to do anything, from buying in goods 
to answering the telephone. B has three clerks, but their 
work is more specialised. B does the buying in himself, and 
each of his clerks has his definite department. His store 
seems to be kept more neatly, and while none of his clerks 
seem to have as wide knowledge about the business as A's 
clerks, each one knows a great deal more in his own particu- 
lar department. When business is slack, his clerks are tabu- 
lating and classifying the goods in their own departments, 
and during the busier part of the day it takes them less time 
to do business than at A's store, because each knows exactly 
what he has in his own department, and can put his hand on 
it at once. In two years' time, A is going out of business, while 
B is enlarging his premises. 

G and D are students in the same college. C attends classes 
and reads his assignments in a general sort of way, but does 
not get much out of his course. He takes things as they 
come along. If he happens to understand a subject easily, 
he passes. If there is any difficulty, he — takes another subject. 
D puts in no more time on his work than C, but he goes about 
it in a different way. He takes notes of what seems impor- 
tant in class, and, in preparing his assignments, makes brief 
analyses, noting down the important points and running them 
over before class. He soon learns what sort of thing to look 
out for, and has little difficulty in mastering each subject he 
takes up. Finally, he elects courses which belong together 
and give him what he wants to get from his college work. 
At the end of his course, he has developed a great deal, while 

197 



198 CHARACTERISTICS OF SCIENTIFIC METHOD 

C leaves college without a degree and with a marked distaste 
for study. 

These instances illustrate the difference between drifting 
along in a general sort of way, and applying scientific method. 
It is the difference between blundering along with a trial-and- 
error method, and finding one's way with a trial-and-success 
method. There is a right way and a wrong way of doing 
anything. The right way is the efficient way which leads 
to success. The wrong way is the inefficient way which leads 
to failure. What is called "scientific method" has arisen from 
a study of the methods which "work," that is to say, which 
lead to success. Such methods have been studied in commerce, 
in art; in the technical, applied sciences, and above all in the 
laboratories in which genuine discoveries have been made. 
Efficient methods of salesmanship differ from efficient methods 
of using tools, and efficient methods of using tools differ again 
from the efficient methods by which the original thinker solves 
his problems. Each branch of work has its specialised appli- 
cation of methods found valuable for its special purposes. 
But it has been found, in spite of these differences of detail, 
that there are a number of general respects in which all such 
methods, whatever the branch of work, agree. It is the sys- 
tematic study of these general characteristics of scientific 
method which will be dealt with in the remainder of this 
book. 

What are the most general characteristics of scientific 
method, the characteristics which all successful workers in 
every field agree in regarding as important? If we ask, what 
the method is, rather than how it should be applied, we find 
that it has two functions which are most generally consid- 
ered of importance. (1) Certain methods are concerned with 
investigation, discovery, finding out something new. (2) 
Certain others are concerned with exposition, explaining to 
others, organising what we already know. Investigation, then, 
and Exposition are the two functions of scientific method which 
are most generally regarded as important. Application comes 
only after the demands of science in the way of investigation 
and in the way of exposition have been satisfied. 

Methods of Investigation (A) Analysis. — What are the chief 
methods employed in investigation? The very first is analysis. 
Before we can solve any problem which is at all complex, it 
is necessary to take stock, as it were, both of what we know 



METHODS OF INVESTIGATION 199 

and of what we do not know but have to find out, with explicit 
reference to the case before us. One of the very first things 
which a recruit learns to do with his rifle is, to take it to 
pieces. One of the first things which a research scientist has 
to do, is to analyse his problem and tabulate his data. One 
of the first things which a physician has to do is, to make a 
list of the symptoms of the patient to whom he is called. 
Before any steps of a more advanced kind can be taken 
towards solving a problem, it is necessary to realise exactly 
what the problem is, what are its conditions, or — as the 
scientist puts it — what are the data. This first step which 
is preliminary to all further work upon a problem, whatever, 
the field and whatever its specialised name — as diagnosis, tak- 
ing stock, tabulating data, etc., — is, in its essential nature, 
analysis. 

(B) Abstraction. — A second general method of investigation, 
analytical in its nature and following closely upon the pre- 
liminary analysis just mentioned, is the method of abstraction. 
Given the analysis of a concrete situation into its general ele- 
ments, it is usually necessary to pick out certain of these 
elements, and set on one side, as irrelevant or at least 
negligible, certain other elements, all of which were equally 
present in the concrete situation with which our analysis 
dealt. This process of picking out from the data those ele- 
ments which are important for some special purpose, and 
neglecting the others, is a method of isolation. By its means, 
we isolate a special group of elements for special investiga- 
tion, and are thus enabled to concentrate our attention upon 
the problem bit by bit, instead of having to deal with it as 
a whole. "Divide and conquer" is true not only in military 
science, but in all scientific study; and this process by which 
we isolate certain elements so that we can solve the problem 
piece-meal, is abstraction. As an example of this method at 
work, we can consider the way in which geometry, which deals 
with the nature of space, does not attempt to study space 
as a whole, but splits up the problem, and begins with a 
study of two-dimensional space, especially with a study of the 
properties of straight lines, triangles, circles, parallelograms, 
etc. So too Aristotle, in writing upon the subject of Friend- 
ship, does not deal with the whole question in a general way, 
but divides it up into friendships of pleasure, friendships of 
business, etc., and discusses each of these in abstraction from 



200 CHARACTERISTICS OF SCIENTIFIC METHOD 

the others. By this method he is enabled to introduce a 
degree of clearness and distinctness into his discussion which 
is the admiration even of present-day thinkers.! 

(C) Determination. — A third general method, following 
closely upon the isolating method of abstraction, is the method 
of determination. Given a narrow group of isolated elements, 
a, fc, c, d, . . . it is possible to proceed further by a care- 
ful comparison of a with b, c, d, . . . resulting in what 
are called new "determinations" of a. When friendship has 
been analysed into the special groups of friendships based 
upon community of purpose in some higher sense, as in moral, 
educational, or scientific collaboration, it is possible to "deter- 
mine" each of these groups further by comparing instances 
viewed in varying circumstances. They can be compared in 
respect of durability, in respect of ethical value, in respect 
of their value for science or art, in respect of economic, social, 
or religious value, etc., and each comparison tends to bring 
out new determinations, until in the end we know far more 
about both elements and groups — and indeed about friendship 
in general too — than we did before this method was applied. 
This method, then, which appears to be less of an analytical, 
and more of a synthetical nature, is known as determination.2 
It leads to definition and classification, though these are usu- 
ally regarded as coming under Exposition rather than 
Investigation. 

(D) Synthesis. — "A fourth general method of investigation 
is synthesis. The word synthesis means putting together, 
and it may be the precise reverse of analysis, as when the 
recruit who has taken his rifle to pieces is taught to put it 
together again by exactly reversing the order of procedure 
by which he took it apart. But an exact reversal of the 
analytical procedure is, in actual fact, somewhat rare. It 
is far more usual to take the elements which analysis and 
abstraction have set before us, and to put these together in 
some order which is new. We may omit certain of the 
elements originally present, on the ground that they are irrel- 
evant and unnecessary, and much of the value of synthesis 

i See Aristotle's Nicomaehean, Ethics, Bks. viii-ix, and the introduc- 
tory remarks of Sir Alexander Grant, in his edition, immediately before 
the beginning of Bk. VIII. 

2 The meaning and value of Determination are especially treated of 
by John Locke, in the second edition of the Essay. See Fraser's 
edition of the Essay, pp. 22-24 



METHODS OF INVESTIGATION 201 

as a scientific method consists in its use in experimentally 
discovering just what may be omitted without prejudicing 
the result. White light is analysed into a mixture of various 
wave-lengths of ether, hut we can synthetically produce the 
appearance of white — e. g., on the color-wheel — by mixing, not 
all the rays of the spectrum, but as few as three or even two 
of the spectral colors revealed by analysis. 

Further, by using the point, straight line, and surface 
revealed by analysis, synthetic geometry can construct any 
number of mathematical forms which are of the utmost 
importance for progress, not merely in geometry itself, but 
in all the sciences which admit of the application of geo- 
metrical methods. That is to say, synthesis is by no means 
limited to the concrete situation from which analysis started, 
but can go beyond it in its new constructions, creating forms 
like the eikosihedron, which is not found in nature, and such 
ideas as a fourth, fifth, or nth dimension of space, which is 
not observed by us. 3 Synthesis, then, is valuable in at least 
three distinct ways: (1) It may be used as a check upon 
analysis, as when we verify analytical results by reconstruct- 
ing the concrete situation. (2) It may be used in the dis- 
covery of simpler, more economical or more efficient methods 
of producing a desired result, as synthetic chemistry con- 
structs substitutes for natural products which are hard to 
obtain. (3) It may be used, as in mathematical construc- 
tions generally, to give us information which reaches far 
beyond our original data, as we see especially in the use of 
graphs. This third use, however, is not by any means con- 
fined to mathematical constructions, but is true generally, 
as every applied science bears witness. 

(D) Synthetical Abstraction and Determination. — A sub- 
form of abstraction is largely of a synthetical nature. There 
is, in addition to the abstraction which isolates elements, an 
abstraction which isolates laws or generalisations from experi- 
ence. It is by the aid of this generalising abstraction that 
we neglect the particular and accidental element in individual 
experiences, and select for especial attention the general or 

3 Such symbolic extensions of ideas originally given in sense-experi- 
ence, are what Docke calls "Modes." Simple Modes are expansions 
of a single idea, as 2, 3, 4, 5. are expansions of the arithmetical 
unit, and Complex or Mixed Modes are formed by uniting different 
ideas, or their expansions, as "running" is a composite, consisting of 
(1) complex movements and (2) the sense of power. Cf. Essay, Bk. 
II, chapters xviii, xxii. 



202 CHARACTERISTICS OF SCIENTIFIC METHOD 

more universal element. This may look as though we were 
isolating the Zaw-aspect of our experiences, and consequently, 
as though the method of generalising abstraction were really 
analytical. In practise, however, it always represents a sum- 
ming up of many experiences, and is thus synthetical. A 
composite photograph, for example, is formed by putting 
together many negatives in order to obtain a single positive. 
The final positive brings out all the elements which the 
different negatives had in common, and omits the elements 
which appear in only one or two negatives. In this way we 
obtain a type-form, and it is obtained by abstraction.* But, 
as resulting from many negatives and summing them up, 
such generalised products of abstraction are synthetical, much 
as a graph — such as the practise-curve, or the memory-curve 
— sums up the results of many experiences and is usually 
regarded as synthetical. That "determination" is largely 
synthetical, we have already stated. These methods of gen- 
eralising abstraction and determination lead naturally to 
classification, but this is generally treated under the head of 
Exposition. 

(E) Induction. — A fifth method of investigation, which 
depends upon both analysis and synthesis in all their forms, 
is induction. By some logicians induction is regarded as the 
investigatory method par excellence. But there can be little 
doubt, from a modern viewpoint, that it is a special form 
which presupposes both analysis and synthesis. A just crit- 
icism frequently leveled at Mill's "inductive methods" objects 
that when phenomena are already analysed into A, B, C, etc., 
— as in his exposition is always taken for granted — the real 
work of investigation is almost completed before the specif- 
ically inductive methods are brought into play; and in gen- 
eral, there can be no doubt that analysis and synthesis are 
more general methods, methods of wider application, and 
that induction proper is somewhat more narrow and specific, 
and presupposes both analysis and synthesis. 5 The typically 
inductive method starts from a concrete situation which has 
already been analysed and further prepared by isolating 

4 Cf. Fr. Gaiton, Inquiries into Human Faculty, Appendix II, pp. 
349-354. 

5 Cf. e. g., R. W. Sellars, Essentials of Logic, p. 216. Cf . also F. H. 
Bradley, Principles of Logic, p. 331, "The discriminative analysis 

. is the real agent which .- . . contains the 'induction.' " 
Also pp. 332-334, 335-336. 



METHODS OF INVESTIGATION 203 

abstraction and by determination, and assumes some hypoth- 
esis or suggested law which is intended to account for the 
concrete situation, and then proceeds to test this hypothesis 
by the method of trial and verification. The inductive method 
thus resembles the second kind of abstraction — generalising 
or synthetical abstraction — except that induction sometimes 
goes rather beyond the data, treating them as a fragment of 
some wider system than what is actually observed in the 
immediate concrete situation, whereas abstraction, as such, 
never goes beyond its data. Induction is thus a process which 
uses, as necessary elements in its construction and verifica- 
tion of hypotheses, the two more general methods of analysis 
and synthesis. 

(F) Deduction. — A sixth and final method of investigation 
is deduction. By some writers deduction is regarded as 
suitable only for purposes of Exposition, the function of 
Investigation being peculiarly the office of induction. But 
a little consideration will show that this can hardly be the 
case. By "deduction" is typically understood the arguing 
from a general principle to its consequences, and in almost 
all subjects capable of being investigated this method is of 
enormous importance. In fact, the typical inductive method 
is known as the ''deductive method of induction," because, 
assuming a hypothesis to account for our data, we proceed 
to deduce what would follow if this hypothesis were true, and 
then compare our deduced consequences with what we find 
empirically to be the case. A student who can reason deduc- 
tively — i. e., can draw conclusions from premises and see into 
what consequences the adoption of a principle will lead him 
— can usually see his way into a problem better than a student 
who has not mastered this method. The importance of such 
methodical insight for solving problems is obvious, and we 
shall accordingly regard deduction as a method of investiga- 
tion. Like induction, it is not independent of analysis and 
synthesis — in fact certain modern logicians tend to distin- 
guish an analytical form from a synthetical form of deduc- 
tion, as methods appropriate to different classes of problems. 

Summary. — Analysis, then and synthesis, abstraction and 
determination, induction and deduction, are the most generally 
recognised methods of scientific investigation. The most wide- 
reaching and the most universally present, are analysis and 
synthesis, but in solving any complex problem, in life or in 



204 CHARACTERISTICS OF SCIENTIFIC METHOD 

science, it is usual to employ every one of these methods. 
Definition and the concept, classification and the organisation 
of systems, are also pressed into the service of investigation. 
But these subjects are usually treated under the head of Expo- 
sition, to which we next turn. 

Forms of Systematic Exposition. — Exposition cannot be 
sharply distinguished from Investigation. In scientific prac- 
tise, there is no form of Exposition which is not frequently 
used in investigating new problems, and there is no method 
of Investigation which cannot be used in systematising one's 
conclusions or in explaining them to others. In fact, some 
of the best expositions are deliberate repetitions of the 
methods by which scientific problems are investigated. The 
laboratory method of studying known scientific laws is of 
this kind, and so is the attempt to understand ethical prob- 
lems by the "case-method,"6 or the study of a poem like 
Kubla Khan, or a book like the Critique of Pure Reason by 
following the Werdegang, the processes through which the 
author passed in coming to write it. 

But in spite of this confusion of methods in practise, a gen- 
eral distinction of purpose can be, and in a discussion of 
logical theory should be, clearly established. In Investiga- 
tion, our primary interest lies in the direction of making dis- 
coveries and reaching important conclusions. In Exposition, 
we are interested primarily in stating those conclusions 
clearly and in systematic connection with other conclusions 
or with general knowledge, and especially in proving to others, 
as well as to ourselves, that our investigations have actually 
succeeded in establishing some principle or in solving some 
problem. Proof and the organisation of what we already 
know are thus the main goals of Exposition, though in attain- 
ing these ultimate aims there are also certain simpler forms 
which must first be considered. 

(A) Definition. — The very first of all, a form of exposition 
presupposed by all organisation of knowledge for purposes 
of either explanation or proof, is definition. In the very 
beginnings of an enquiry or of an explanation, it is advisable 
to lay down and determine certain lines along which the 
enquiry or explanation is to proceed. This is the function 

6 Cf . G. C. Cox, The Case Method in Ethics, Journal of Philosophy, 
Psychology and Scientific Methods, Vol. XI, 1914, pp. 16-23. Cf. Vol. 
XIII, 1916, pp. 212-213. 



FORMS OF EXPOSITION 205 

of a preliminary definition. In fact, definition means, draw- 
ing the lines which separate one direction of thought from 
another, delimiting a field of enquiry or explanation, stating 
what an object is in such a way that we can place it roughly 
within a system of problems or within some special depart- 
ment of knowledge. This latter portion of the meaning of 
definition is exemplified especially at the end of an enquiry 
or explanation, when we conclude with a clear-cut and more 
final idea of the object studied. Such a result of final defini- 
tion is known as a concept. Definition, then, has a place both 
at the beginning and at the end of a process of enquiry or 
explanation. A preliminary definition tends to emphasise 
rather the elements which together make up the object 
studied, and the concluding definition tends to emphasise 
rather the principle of construction, in accordance with 
which the elements can be put together. In any case, how- 
ever, the function of definition is fundamental in exposition. 
In order to classify, we must know definitely what the ele- 
ments to be classified are — i. e., we presuppose that they are 
defined. So too in order to prove any proposition, we must 
know definitely what we wish to prove and what elements 
play a part in the argument — that is to say, 'proof also pre- 
supposes definition. In general, then, definition is a form of 
exposition which we must regard as fundamental, as a neces- 
sary pre-requisite of all the more complex forms of exposition. 
(B) Classification. — A second form of exposition which is 
closely connected with definition is classification. In investi- 
gating or in expounding, we find it helpful to group together 
a number of kindred elements so as to form a single group 
or class. When we can place some object of study in its 
proper context, when we can assign it to some class of which 
something is already known, we at once feel that we know a 
great deal about that object. If we know that a Mr. Smith is 
to deliver a public lecture, we do not feel more than mildly 
interested. He is only "a Mr. Smith" to us. But if we learn 
that he is a distinguished author, and a prominent Democrat 
or Republican, we at once know much more about him. If 
we learn further that he is an official representative of a 
certain group of interests, and that he is to speak on behalf 
of these interests, his meaning and value for us as an author- 
ity on his subject are increased, and we may go and listen 
to his address. In this way, then, we classify or arrange 



206 CHARACTERISTICS OF SCIENTIFIC METHOD 

objects in groups, because they thus throw light upon one 
another, whether for purposes of investigation or for pur- 
poses of exposition. We find that to put together objects 
which logically belong together — i. e., objects which belong to 
the same universe of discourse, or have kindred meanings — 
is a great help both in acquiring and in transmitting knowl- 
edge. 

(C) Proof. — A third form of systematic exposition is proof. 
To prove, whether to ourselves or to .others, is so important 
a part of logic, that some of the older text books did not hesi- 
tate to define their study as the "science of inference and 
proof." In a sense, every method of investigation which 
reaches a valid conclusion is a kind of proof, and it is some- 
times stated that in Euclidean geometry the genuine proof is 
already given in the construction. But the formal proof 
which justifies the construction to others — or to oneself — 
usually follows other paths, and tends to consist in showing 
that what seems strange or novel about the theorem in ques- 
tion really follows from, or is logically of a piece with 
theorems or propositions previously understood and accepted 
as valid. If direct insight has not been attained, a form of 
argument known as indirect proof is sometimes used. This 
resembles the reductio ad absurdum arguments. We show 
that the opposite of the proposition which we wish to prove 
leads to conclusions which do not fit in with what we already 
believe on the subject in question, as Herbert Spencer seeks 
to prove that pleasure is an important ethical good by show- 
ing that its opposite, pain, is universally regarded as an evil, 
and that to suggest that we should seriously pursue pain is 
inconsistent with all that we believe of human motives.? Indi- 
rect proof is seldom as satisfactory as direct proof, but there 
are almost always many lines along which we can advance to 
a definite proof, and sometimes methods which seem more 
roundabout and indirect are found more satisfactory and con- 
vincing in the end. This is the case especially where some 
science is still in its earlier stages, and insight into its sub- 
ject-matter is still largely to seek. Needless to say, proof 
uses all the methods of analysis and synthesis already con- 
sidered, and may be either deductive or inductive, according 
to circumstances. 

* S-ee Spencer's Data of Ethics, chapter iii, esp. p. 22. Spencer's 
test of the truth of any proposition is known as "the inconceivability 
of the opposite." 



FORMS OF EXPOSITION 207 

(D) System of the Sciences. — These three, then — definition, 
classification, and proof — are the chief forms of systematic 
exposition. It is usual, however, to add to a study of these 
forms some consideration of the ideal towards which exposi- 
tion tends — viz., the natural system of the sciences — as a con- 
crete account of the kind of knowledge at which scientific 
method, in the forms of investigation and exposition, aims — 
the knowledge which in its applied forms aims at enriching 
our practical life with all the resources which intellect can 
muster for the service of society. 

Summary. — The general characteristics of scientific method, 
then, vary according as the aim is investigation or exposi- 
tion. The methods of investigation are analysis and synthe- 
sis, abstraction and determination, induction and deduction. 
The chief forms of systematic exposition are definition, classi- 
fication, proof, and the system of the sciences. It remains to 
study each one of these general characteristics of scientific 
method, in the chapters which follow. 

FOR FURTHER READING 
s 

W. Wundt, Logik, (3rd Edit.), Vol. II, pp. 1-2, 38-40. 

EXERCISES 

1. What are the chief differences between scientific and unscientific 
method in the following cases : (a) In purchasing household furni- 
ture, (b) In receiving and answering letters. (c) In studying a 
foreign language? 

2. Show how analysis, abstraction, and the other methods of 
investigation might be applied in the following cases: (a)- In choos- 
ing a career. (b) In estimating and judging character. (c) In 
research work (in a laboratory science, or in a literary or historical 
science). 

3. Show how definition, classification, and proof could be used 
in the following cases : (a) In writing an essay on the value of 
travel in broadening the mind, or on the unaccountability of tastes, 
(b) In teaching elementary algebra or geometry to a high school 
class, (c) In explaining to a friend how to repair a minor injury 
to his automobile, or how to study efficiently for examinations. 



CHAPTER XIX 

ANALYSIS 

Divide et impera is the motto of analysis. A music student 
who wishes to master the difficulties of some study does not 
practise the study as a whole, hut splits it up into subjects 
or even phrases and practises these, one by one, first with the 
right hand alone, then with the left hand alone, and finally 
with both hands together, paying the utmost attention to 
every detail. So too a recruit learning the manual of arms 
divides the more complex movements into a number of ele- 
mentary unit-movements, and practises every detail of these 
movements separately in order to present a good appear- 
ance at drill. So also in carrying through a nation-wide cam- 
paign, whether for political, economic, or religious purposes, 
the country is divided into a number of divisions, each of 
these divisions into districts, each of these districts into sub- 
districts, until finally the whole territory is parcelled out in 
such a way that one or two campaigners are responsible for 
each block or ward. In short, whether the aim is success 
in winning battles, or success in any other large and complex 
purpose, analysis is the first and most universal method 
adopted. 

Nature of Analysis. — What exactly is analysis? Perhaps 
we can obtain the best mental picture of what is meant in the 
following way. Imagine a bundle of sticks, fastened together 
by a rope. If we untie the rope, the bundle falls apart into 
its constituent elements — the sticks. Analysis means pre- 
cisely that — untieing or loosening up — and no more. Analysis, 
as such, introduces no new purposes, and is concerned with 
no ulterior motives. It simply looses the bonds of connec- 
tion and lets the material thus set free from what held it 
together fall apart as it will, whatever elements happen to 
be there. It is absolutely vital to the method as scientific 
that this should be so — that the material should be permitted 
to fall apart in its own way, into its own elements, and 
that there should be no interference in the way of suppression 

208 



NATURE OF ANALYSIS 209 

or addition, no re-arrangement, no selection or introduction 
of a prejudiced or arbitrary viewpoint. The sole aim of 
analysis is that the connection should be loosed and the 
material fall apart into its constituent elements. The bundle 
must cease to exist as a bundle. We must have in its place 
a number of sticks and a piece of rope — preferably without 
the slightest suggestion of their ever having formed a bundle 
or being usable in any special way, in order that the subse- 
quent examination may be absolutely free from subjective 
coloring or prejudice, and can proceed to deal with the 
objects objectively. 

The Aim of Analysis. — There is thus an aspect of will, pur- 
pose, or design, in analysis. We intend in the first place that 
the material shall actually fall apart, and shall fall apart 
into elements or units, portions which can be regarded as — 
at least for oar purposes — ultimate. We intend, that is, that 
the analysis shall not in any way fail, but shall be carried 
right through to its logical conclusion. Analysis is to be com- 
plete. There must be no residuum which obstinately defies 
our efforts at analysis, but the whole must be taken apart 
without remainder. In the second place, we intend that the 
material shall fall apart into elements which are its own, that 
the bond of connection which we loose shall really be the 
bond which in fact holds together the elements in question. 
We intend to follow natural lines of cleavage, to divide up 
the object in accordance with its own nature, its own law 
of connection. Analysis is to be objective. We intend that 
analysis shall not fail by containing elements which are ficti- 
tious, mental fictions, fanciful, arbitrary, subjective, but that 
it shall cross the line which divides the fictitious from real, 
the subjective from the objective, and shall deal with the 
actual nature of the actual object. Completeness and objec- 
tivity — these represent the aim of analysis. 

How far Realisable? (A) In Man-Made Structures and 
Mental Models. — How far can this aim be realised? Let us 
consider. A recruit is shown how to take his rifle to pieces. 
By turning here and pulling there he can take it to pieces 
in a way which is objective — for the striker, follower, main 
spring, etc., are actual parts of the actual rifle. But his 
analysis is not complete. By the use of a screw-driver, the 
armorer will take the rifle still further apart, until he has 
reduced it to its last elements. His analysis is both objec- 



210 ANALYSIS 

tive and complete. So too, the use of a screw-driver and a 
wrench, plus the methods of pulling, pushing, and turning, 
will suffice to take to pieces a type-writer or piano, complex 
though these objects are, and such an analysis can be not 
only objective, but also as complete as we please. In fact, 
any machinery which the mind of man can devise, the mind 
of man can also take to pieces. Artefacts, then, i. e., man- 
made objects fashioned in accordance with some rational plan, 
can be analysed in a way which is both objective and com- 
plete. 

Let us consider another class of cases. A complex arith- 
metical example can be reduced to a number of simple opera- 
tions with units. A complex geometrical figure can be reduced 
to a combination of simple lines and points. And generally 
speaking, mathematics presents us with a host of complexes 
which the mind of man can take apart because the mind of 
man has put them together, and put them together in accord- 
dance with a rational plan, — a plan which the mind of man 
can understand. These cases are, in fact, typical of the vast 
number of thought-structures to which we have referred as 
mental models. Whatever reason has constructed in accor- 
dance with its own laws, reason can take to pieces again in 
a way which is both objective and complete. Whatever has 
been constructed in accordance with intellectual standards or 
intellectual demands, can be analysed in accordance with 
intellectual demands, and speaking generally we can say: 
Whatever is rational can be analysed, and can be analysed 
just so far as it is rational, whether it is a mathematical 
problem, a carefully thought-out plan of life, an esthetical 
composition, or a piece of mere machinery. In such cases, 
where thought apprehends the structure which thought has 
itself introduced in accordance with its own laws, i. e., where 
thought is dealing ultimately with itself — analysis, as we 
have described it, is possible. In such cases we can realise 
the aim of objectivity and completeness. 

It remains to consider a further point. Whatever is rational 
can theoretically be analysed. But in order that this theoret- 
ical possibility should be realised, we must know something 
more. It is necessary to understand the special law of con- 
nection which binds together the elements in question so as 
to constitute a rational complex. Without insight into this 
law, we cannot know what are elements and what are not, 



AIM OF ANALYSIS 211 

in a given case. We do not know what to look for. Let us 
suppose that we receive a message in cipher: "AAABBBAAB 
ABBBAAAAABBBBAAABBAABBBBAABBAAABABABBBAA 
BBAABABAAABAAABBBAAAA." Here is something con- 
structed in accordance with a rational plan. But without the 
key, what can we do? Suppose we analyse it into letters. 
That will not help us. For unless the cipher is constructed 
in such a way that each single letter corresponds to some 
single letter of the alphabet, our analysis is irrelevant. We 
are analysing into elements which are not elements of the 
cipher, but are arbitrary. They are, indeed, in a sense com- 
plete; for nothing is omitted. But such an analysis is cer- 
tainly not objective — i. e., does not analyse the object, the 
cipher itself, at all. As there are only two letters, A and B, 
it is plain that the single letter idea must be abandoned. We 
try again. Perhaps A represents one letter of the alphabet, 
AA another letter, AAA yet another, and so also with B, BB, 
BBB, etc. The most frequently occurring of these combina- 
tions are AA and AAA. But here again we fail, and our 
failure shows that the principle in terms of which we are 
trying to analyse is not the right one. We try again. Per- 
haps some combination of A's and B's is equivalent to each 
letter of the alphabet. We may remember having read of 
Bacon's bi-literal cipher, or we may add up the total number 
of letters and find that they will divide by five, and thus, 
even without knowledge of Bacon, assume that a group of 
five letters, consisting only of A's and B's, corresponds to 
a single letter of the alphabet. Our assumption may be cor- 
rect, but of itself does not suffice for the solution of our prob- 
lem. We cannot be sure that the analysis is correct, and 
that AAABB, BAABA, etc., are the genuine elements of the 
cipher, until we have discovered more. We try constructing 
a cipher in accordance with the formula with which we are 
now experimenting. Let a = AAAAB, b = AAABA, c = 
AABAA, etc. There are, of course, many possibilities here, 
but we try the first one, and find — after a few more mistakes 
and trials — that it fits. Now that we can finally read off the 
message, and thoroughly understand the principle of construc- 
tion, we can analyse our problem into its elements in a way 
which is both objective and complete. What is neeeded in 
order to realise the aim of analysis is (1) that the object 



212 ANALYSIS 

should be constructed in accordance with some rational plan, 
and (2) that we should have insight into the plan. Other- 
wise, our efforts at analysis are irrelevant, and fail from the 
viewpoint of objectivity at least. Such attempts are imper- 
fect and artificial. 

(B) In Dealing With Natural Phenomena. — Our procedure, 
in such cases as the above, is like that of a person who stands 
before a locked door with a bunch of keys, one of which is 
the right one. He tries key after key, until he comes upon 
the right one. So too we tried one mental model after 
another, until we hit upon the one which exactly fitted. But 
we must now advance to a further consideration. In the 
cases hitherto considered, thought is dealing with its own 
constructions, its own instruments, forged by itself in 
accordance with its own laws. In actual practise, however, 
it is very rarely that thought either needs or wishes to analyse 
itself and its own constructions. Thought-structures are 
instruments intended to solve problems which face us in 
life — problems in the objective world, and in dealing with 
concrete situations it is a question whether any mental model 
will "fit" except very roughly and approximately. Analysis 
is imperfect — i. e., we have to use models arbitrarily chosen, 
and thus not perfectly appropriate — (1) when we do not know 
the principle which governs the situation before us. In actual 
practise, this is almost always the case. A specialist is asked 
to psycho-analyse a hysterical patient, with a view to finding 
out what is wrong. No one knows. He proceeds to test for 
all the frequent "complexes," until he hits upon a group of 
associations which seems to be causing the trouble. This is a 
lengthy process, and the preliminary attempts at analysis are 
largely irrelevant and, in some cases, even misleading. But 
further, analysis is imperfect (2) when our instruments are 
not perfectly adapted to their work. The various diseases, 
physical and mental, which a physician has to diagnose, are 
cases in point. Every one knows that the most terrible mis- 
takes sometimes take place. Where the symptoms are not 
accurately studied, it is possible for the physician to analyse 
in terms of a mental model which seems partially to fit the 
case, but in fact is tragically beside the point. Thus typhoid 
patients have been actually treated for appendicitis, cancer 
has been treated as indigestion, and mental disease has 



METHODS OF SCIENTIFIC ANALYSIS 213 

received any and every kind of treatment, from religious ven- 
eration to imprisonment or a sound thrashing.* 

In dealing, then, with objects other than our own thought- 
constructions, — that is to say, in the face of nature with its 
infinite variety of problems — we are necessarily restricted to 
the trial-and-error method, and to experimenting with ana- 
lytical models which we know to be more or less imperfect. 
The result is, that our conclusions never perfectly apply to 
their material, and in consequence, our analysis is hardly ever 
complete. There is almost always some residuum which obsti- 
nately defies further analysis. A chemist, analysing given 
material for traces of poison, knows that there is always a 
certain residuum for which he cannot perfectly account. Dif- 
ferent chemists analyse the same material but come to differ- 
ent conclusions: A finds 5% of the poison, B finds 6%, and 
in certain cases such differences are important. Where our 
instruments are not perfectly adapted to their material, our 
analysis cannot but be imperfect, and, as contrasted with our 
perfect success in dealing with mental constructions, we can 
say that scientific method, when applied to physical or nat- 
ural-science problems, is always partly incomplete, and never 
perfectly objective. We deal, not with things as they are in 
their nature, but with mental models whose structure we 
understand, and the difference between the mental model and 
the actual given situation is the unanalysed residuum which 
is the measure of our practical success or failure. If the dif- 
ference is large, we fail. If it is negligible, we succeed in prac- 
tise. But a theoretically perfect analysis of natural phe- 
nomena is an unattainable ideal. 

METHODS OF SCIENTIFIC ANALYSIS 

(A) Mathematical. — But because our efforts at analysis are 
empirical and imperfect, it does not follow that we cannot at 
least approximate to results which we can accept as satisfac- 
tory. Even mistaken experiments succeed, as a rule, in assist- 
ing us to some insight into the problem studied. In the case 
of the cipher, which we analysed above, we gradually worked 
our way to a method which was satisfactory. So also in nat- 
ural science. We almost always begin with some method of 

i Cf. Bernard Hart, Psychology of Insanity, chapter i. 



214 ANALYSIS 

analysis which we know to be merely preliminary, because 
experience shows that it is helpful in preparing the material 
for a more final kind of analysis, and in giving us a kind of 
insight which, without such preliminary analysis, we lack. 
Thus, in attacking many a psychological or sociological prob- 
lem, while we know that the only kind of analysis which can 
yield us final satisfaction will be specifically psychological or 
sociological, we begin with an analysis which is mathematical. 
In all the natural sciences, mathematical analysis is an aux- 
iliary method of the greatest importance. So far as it goes, 
it is sufficiently exact, and it tends to leave the material in 
better shape for a more final analysis. For instance, how long 
should a Dachshund of given girth, head, and tail, be in the 
body in order to give the most esthetical satisfaction? For 
experimental purposes, a model Dachshund is used, made of 
celluloid, the body of which can be elongated or contracted by 
means of an apparatus which admits of exact measurement in 
terms of a millimeter scale. Starting with a short Dachshund, 
we observe it as it is gradually lengthened, until we feel that 
it is just right. A record is taken of the measurement, and 
we try again. After many such attempts, we commence with a 
Dachshund which is much too long, observe it as it grows 
shorter, until we feel that it is just right. Finally, the aver- 
ages of the various measurements are taken, and, after a num- 
ber of mathematical manipulations of the mathematical data, 
we reach certain conclusions as to the variability of the 
esthetical judgment, and also as to certain of the conditions 
which influence it. Such an analysis does not take us very 
far, and experimental esthetics generally is still in a very 
preliminary stage, but still, a beginning has been made, and 
has been made by using methods which are, at least in part, 
mathematical. 

So too with problems which are sociological. Is there really 
any definite connection between drink and crime? Is imbe- 
cility hereditary? What factors govern the increase or 
decrease of population? In studying such problems, mathe- 
matical analysis is vital. Without statistical methods of con- 
siderable refinement, the material could never be reduced to 
a form which the scientist could use. This is true also of 
intelligence tests, tests of bodily efficiency, and generally, in 
all cases which admit of the application of mathematical 
methods of analysis. Breaking up a vast and complex situa- 



METHODS OF SCIENTIFIC ANALYSIS 215 

tion into elements which can be counted and shifted around 
in accordance with quantitative methods is almost always 
helpful in adding to our insight into the structure of a con- 
crete problem.2 

(B) Causal. — A second mental model which experience simi- 
larly shows to be helpful in approaching the analysis of a con- 
crete situation is the cause-and-effect principle. This is found 
helpful in analysing processes, events, and generally any phe- 
nomena which occupy time. Mathematical models are also 
employed as a rule, because of their value as auxiliary meth- 
ods. But in dealing with processes and events, we tend to 
split the phenomena up into groups which are not so much 
1, 2, 3, . . . , as before-and-after groups, antecedents and 
consequents, cause-and-effect groups. The physician called in 
to diagnose a case begins, it is true, by listing the symptoms. 
But his analysis throughout has less of mathematical, and 
more of causal reference. The enumeration of symptoms is 
less important as enumeration — i. e., mathematically — and 
more important as throwing light upon causes, as a sore throat 
followed at a certain interval by a rash implies scarlet fever 
or measles, or as certain disturbances of digestion imply 
decayed teeth, etc. So too a professional man, in analysing 
the noises which disturb him at his work, is not content with 
a mere enumeration, but analyses with a very definite causal 
reference. Thus, freight-train disturbances point to increas- 
ing traffic, and thus to prosperity; passing automobiles, 
whether for business or pleasure, seem to point in the same 
direction; while certain other noises point to causes which 
should, in his opinion, be eliminated. In fact, during the 
greater part of our waking life we are analysing with this 
kind of causal reference all events which attract our atten- 
tion, and all persons with whom we are brought into con- 
tact. On the whole, then, it seems legitimate to regard these 
two classes of mental patterns, the mathematical and the 

2 Experience with card-index methods will justify this statement. 
It is stated by some logicians (e. g., Bosanquet and Wnndt), that the 
body of science which constitutes Law does not use mathematical 
methods of analysis, as it is not quantitative. This does not seem 
to be exactly the case. In analysing a concept under various heads, 
it is usual to enumerate the heads of characteristics 1, 2. 3, etc., 
and in all analysis in which card-index methods or anvthing of the 
sort are employed, there is a tendency to treat each record as a "unit." 
and in the shufflings and regroupings of these records, certain methods 
are used which are. to some extent at least, mathematical. It is true, 
however, that in theory and practise of Jurisprudence, mathematical 
methods play a part which is at best only subordinate. 



216 ANALYSIS 

causal, as the most universal and the most helpful of all our 
preliminary and imperfect methods of scientific analysis. 

Validity of Methods of Scientific Analysis. — The mental pat- 
terns employed in scientific analysis, as exemplified in quan- 
titative and causal explanations, are in part inadequate. But 
on the whole, they are found helpful in giving us insight into 
the structure of natural phenomena. On what does this help- 
fulness depend, and how far can we feel justified in approach- 
ing nature in the attitude of a judge, and compelling her to 
answer our carefully prepared questions? To this query, there 
is only one answer which we can regard as admissible. Our 
analytical methods are justified only so far as they are found 
intelligible on the one hand, and found to "work" on the 
other. They should not only be intelligible in themselves, and 
form part of a consistent system of similar mental models, but 
should also be justified in terms of sensory experience.3 They 
should approximate to the completeness and objectivity which 
are such conspicuous features of our analysis when thought 
examines only its own constructions. So far as our empirical 
analyses fall short of these standards of completeness and 
objectivity, so far these serve as encouragements to pursue and 
follow our path yet further, and it is only by continued and 
unwearied experimentation that we come to adjust our mental 
models more closely to the empirical facts, and thus approxi- 
mate more and more to a validity which, in dealing with nat- 
ural phenomena, appears to be beyond our reach. 

Summary. — So far then, we have seen that analysis is a 
preliminary portion of scientific method, and that its appli- 
cation is universal. Its aim is, to loosen the bond of con- 
nection which holds a problem together, and let it fall apart 
into its elements along natural lines of cleavage, in a way 
which is not only objective, but also complete. This aim can 
be realised in dealing with mind-made structures, and with 
these only 4 In dealing with natural phenomena, we can only 

3 For an example of what to avoid, the student with grounding in 
psychology is recommended to glance over J. Chr. Wolff's Psychologia 
Empvrica. The mental patterns are clear and form a wonderfully con- 
sistent group as a whole, and yet there is perhaps not a single problem 
or theorem in the whole book which would be accepted by a present- 
day empirical psychologist. It is weak on the empirical and sensory 
side. 

4 Machines are regarded, from a logical viewpoint, as mind-made 
structures. It is only so ifar as they are made strictly in accordance 
with our mental patterns that we fully understand them. Cf. Bosan- 
quet, Essentials of Logic, p. 125, who treats a portion of a railway 
track as a materialised disjunctive judgment. 



EXERCISES 217 

approximate to an accurate analysis by experimenting, and 
trying whether this mental model or that will apply. The 
most universally usable and the most generally helpful of 
such mental patterns are the mathematical and the cause-and- 
effect models. Though not perfectly satisfactory, they can 
still be accepted as trustworthy so far as they are found to 
"work," and to bring us into closer touch with, and under- 
standing of, concrete problems. By such means we can hope 
for a gradually increasing insight into the structure of phys- 
ical phenomena, and, indeed of all phenomena whatever which 
can be analysed in this way. 

FOR FURTHER READING 

W. Wundt, Logik, (3rd Edit.), Vol. II, pp. 2-8. 

EXERCISES 

Show what part is played by analysis in dealing with the following 
cases: (1) In learning to play tennis or golf. (2) In making one- 
self popular. (3) In finding out what is wrong with an automobile 
which suddenly refuses to work. (4) In finding one's way about a 
new city. (5) In looking up facts or dates in the encyclopedia. (6) 
In securing a position. 



CHAPTER XX 

SYNTHESIS 

"Putting two and two together" is one of the most impor- 
tant of all our intellectual activities. Without this function, 
we should be imbeciles, unable to hold more than a single 
idea in our minds at a time and incapable of performing the 
slightest service for others, or even for ourselves. With it, 
we have an instrument which is indispensable in every walk 
of life. By its aid we construct our daily plans, our science, 
our art, and our religion. Our whole political and economic 
life rests upon it, and so vital does it appear in our reasoning 
processes, that philosophers like Aristotle and Kant have 
regarded synthesis as the most characteristic function of 
mind, and psychologists like Binet and Yerkes rank synthetic 
ability as evidence of advanced intelligence.! 

Nature of Synthesis. — What precisely do we understand by 
"synthesis"? It is the opposite of analysis. Analysis takes 
apart. Synthesis puts together. Given a concrete situation, 
analysis reduces it to separate elements. Given separate 
elements, synthesis reduces them to — what? Let us consider. 
Defends, a, his, dog, master, good, bravely. Here we have 
a number of separate elements. Synthesis puts them together 
in such a way that they make sense — i. e., in such a way 
that they express a certain unity of meaning. "Two N's, 
two O's an L and a D," says the child, "Put them together 
and spell them to me." Here again, it is a question of putting 
them together so that they form a rational unity. Analysis, 
we remember, meant, not merely taking apart, but loosening 
a bond of connection, the principle which held together the 
phenomenon studied. Synthesis, then, means, not merely 
putting together, but introducing some unifying plan, some 
rational principle of connection, so that in place of a mere 
aggregate or disconnected heap we have a genuine totality, 

i Cf . Yerkes-Bridges-Chadwick, A Point-Scale for Measuring Mental 
Ability, 1915. 

218 



AIM OF SYNTHESIS 219 

an organised whole composed of elements which are united 
— i. e., belong together and constitute a single entity, an 
individual. 

Aim of Synthesis (A) Objectivity. — Synthesis means, then, 
no merely mechanical juxtaposition, but a putting together 
which really puts together, so that the elements which are 
synthesised enjoy a genuine togetherness, and constitute a 
unity which is rational. It means intelligent construction, 
rational organisation, and involves the application of intel- 
lectual principles to elementary data. Synthesis aims, then, 
at organisation of the data, and at an organisation which is 
rational. It also aims at organisation of the data. That is 
to say, like analysis, it aims at objectivity. No rational 
person would attempt to construct a triangle out cf tones 
or a melody out of straight lines. In every case the principle 
of unity which synthesis introduces must unify the elements 
with which we start, and must bind them together in a way 
which is suited to their nature. Otherwise we fail in respect 
of objectivity. 

(B) Completeness. — Can we say that, like analysis, syn- 
thesis also aims at completeness? Let us consider. At a 
rational completeness it certainly does aim. For this is 
involved in the very notion of objectivity. Thus, given the 
barrel, stock, magazine, cocking-piece, etc., — i. e., the ele- 
ments out of which a Springfield rifle is constructed — there 
is only one rational way of assembling the parts. If they are 
to form the unity for which they are adapted, it will be neces- 
sary to omit nothing, but to include every single element. 
So too, given the requisite number of automobile parts, there 
is only one way in which these also can be assembled so as 
to constitute a genuine unity — the unity for which they are 
objectively adapted. No single part can be omitted. The 
synthesis must be complete. 

That is to say, where the objective elements are such as 
to render it possible, the synthesis should be complete. But 
there are two other possibilities. The given material may 
contain elements which are too many or too few. Out of an 
assortment of materials taken from several old cars, a skilful 
mechanic will assemble a single car which can be used. But 
he will not have used up all the material. It contains parts 
enough, and more than enough, for one good car, but not 
enough for two. The surplus parts are thus omitted, and 



220 SYNTHESIS 

the synthesis is not, in this sense, complete. But if we 
understand by "completeness" a due regard for objectivity 
and for what is reasonable in the particular situation, we can 
say that even in such cases our synthesis aims at all the 
completeness which could reasonably be demanded. So 
again where the elements are too few. In such cases, it may 
be impossible to put them together objectively — e. g., if some 
vital connecting portion is missing. But in all such cases 
our aim is at completeness. Wherever possible, we piece 
out the imperfections of our material, and construct, as well 
as we can, in all its completeness, the totality, of which our 
data constitute fragmentary portions. 

We may here note a certain difference between analysis 
and synthesis. Analysis seems to be confined exactly to its 
data. Its aim is thus to omit no element, whether relevant 
or irrelevant, and to add nothing, whether some vital element 
has been omitted or not. Synthesis, on the contrary, seems 
to be a more flexible and a more developed method than 
analysis. It can omit what is irrelevant or superfluous, and 
can add what is missing, or at least is imperatively demanded 
by the data in order to put them together. That is to say, 
synthesis can take account, to a greater extent, of rational 
considerations, and is not so tied down to its material. But 
in general its aim resembles the aim of analysis, in that it 
desires above all things objectivity and completeness. 

How Far Realisable? (A) With Mind-Made Entities. — Give 
a child the parts of a jig-saw puzzle, or such letters as 
N, A, T, H, S, 0, G, W, I, N, and ask him to put them 
together. Give an adolescent a box with various compart- 
ments, of which one contains the parts of a simple bell, 
another the parts of a simple lock, etc. Within a reasonable 
time, the child will have put together the parts of the jig-saw 
puzzle or the letters of the name, and the adolescent will 
show you a complete bell, lock, etc. So also a clock maker 
will assemble the parts of a clock, a trained mechanician 
will assemble the parts of an automobile, etc. In a word, 
wherever we have the parts of some mechanism devised by 
the human mind, the human mind can learn to put those parts 
together in a way which is both objective and complete. The 
history of invention further shows that synthesis can in 
many cases improve upon the original principle of construe- 



AIM OF SYNTHESIS 221 

tion, by designing models which use less material, fewer and 
simpler parts, and in a word are more economical and efficient. 

Let us consider other cases which are mind-made, but less 
closely connected with physical matter. Given three straight 
lines, of which any two are together greater than the third, 
it is possible, upon a plane surface, to construct a triangle. 
Given the elements essential for the solution of a problem in 
simultaneous equations, it is possible to solve that problem. 
Given the concept of Man as finite, imperfect, and dependent, 
and the concept of God with the traditional attributes of abso- 
lute power, absolute knowledge, absolute wisdom, etc., it is 
possible to construct a whole system of ethics based upon the 
relation of Man to God. If these instances are typical of 
mental models,, we can state that whatever elements are 
capable of being put together in accordance with a rational 
principle, admit of a synthesis which is objective and com- 
plete. 

In such cases, then, it is theoretically possible to realise 
the aim of synthesis. But before the aim can in fact be 
actually realised, something more is necessary than elements 
which are rationally unifiable. Take any college graduate 
and show him one of the standard puzzle-boxes. Give him 
the following instructions: — "Pull out this lever as far as 
possible. Then pull out this second one. Then stand the 
box upon the side which is painted white. Then turn the 
combination lock twice to the right, to the number 47, then 
twice to the left, to the number 36, then once more to the 
right, to the number 14, and the door will open." The data 
here are the particular instructions, and the problem is, to 
put them together correctly. In theory, the synthesis can 
be both objective and complete. In practise, however, the 
average college graduate will be unable to put together the 
elements of the instructions and hold them together in his 
mind. Either he omits to stand the box upon its white side, 
or he fails to turn the combination lock twice to the left, etc. 
That is to say, he has failed to grasp the rational principle, 
in terms of which the instructions form a unity. In order 
to succeed, it is essential to grasp the principle thoroughly, 
and to apply it exactly. So too, after hearing an address, we 
find that we can perhaps remember parts of what we have 
heard, but that we cannot put the parts together so as to 
form a rational unity — we have lost touch with the principle 



222 synthp:sis 

which made the connection and sequence of thoughts clear. 
So too in carrying through our life-plans, there are times 
when we lose sight of our guiding principles. In such cases 
we find ourselves unable to make sense of our experience, 
and we blunder along at haphazard. In order, then, that the 
aim of synthesis may be realised, it is necessary, not only 
(1) that the data shall be rationally unifiable, but also (2) 
that we thoroughly understand the rational principle which 
is the key to their synthesis in practise. Then, and then 
only, can we advance to a synthesis which shall be both 
objective and complete. 

Just what is our procedure when we are without insight 
into the principle of connection? Let us consider an instance. 
Hour, for, we, early, at, park, an, started, the, of, morning. 
Here we have a number of elements which can be put together 
so as to make sense. How do we synthesise them? We read 
over the given words, and try out various plans for connecting 
them. Something about Parle and Morning. . . . "The 
park in the morning. . . ."? No, we cannot make sense 
that way. We try again, bringing in Hour and We. "In an 
hour we started for the park at early morning. . . ."? 
No — our synthesis is wrong. We have added the word In. 
We try again, joining up Hour and Morning, and this time — 
perhaps after one other mistake — we have it. That is to say, 
we use the trial-and-error method. We adopt tentatively one 
mental pattern after another, until we find one which fits. 
Then, and then only, when we have acquired insight into 
the principle of connection, do we succeed. 

(B) With Natural Phenomena. — In dealing with subjects 
of study other than our own thought-made structures, we 
are almost always in this difficulty. We do not have an 
exact insight into laws of connection, and the greater part 
of the scientific work is directed towards finding out, as 
nearly as possible, what these laws are. We experiment with 
our mental models, one after another, until we gradually 
attain to a certain degree of insight. Thus, when brought 
into contact with an interesting stranger, we note all his 
peculiarities, and then try to put these together in a way 
which will give us insight into his character. The optimist 
tends to synthesise in terms of prevailing bias, and to see 
everyone as better, perhaps, than he is. The pessimist simi- 
larly sees people somewhat worse than they are, and in 



AIM OF SYNTHESIS 223 

general, a little consideration will assure us that, when faced 
with a problem for synthesis, we combine the data experi- 
mentally, in terms of mental patterns which we understand 
and regard as helpful. 

There is, however, a certain difference between thought- 
structures and natural phenomena. In dealing with thought- 
structures we know that there is a key, and the sole problem 
is to find it. In dealing with natural phenomena, on the 
other hand, we assume that there may be a key, and a study 
of the history of science will convince us that we can, at best, 
only approximate to discovering a genuine law of connection. 
The process of experimentation is more prolonged, and we 
must not expect it to lead to a conclusion which will be per- 
fectly satisfactory. We use the best mental models which we 
know, and there is no doubt that we find these helpful in put- 
ting together the data of our various problems, but when all 
is said and done, the mental model differs in its structure 
from the actual phenomena, and this difference represents an 
unknown amount of marginal error. Thus, in dealing with 
our fellow-men, we can proceed on the hypothesis that they 
are all self-centered — egoistic hedonism is the technical name 
for this model — and in general our constructions based upon 
this principle will be sufficiently like the structure of actual 
motive-complexes to "work/' But a wide experience of men 
as well as a less crude psychological theory will show us that 
the self-interested man who always acts upon calculation of 
what will be most to his advantage is a myth — i. e., a mental 
fiction, and is not found in nature. 2 Our models, then, are not 
perfectly reliable, and in point of objectivity we can hardly 
hope to realise the full aim of synthesis. We construct some- 
thing which always differs from what we wish to understand, 
and cur mental model never quite fits into the world of actual 
phenomena. 

So much for objectivity. What are we to say of complete- 
ness? The case resembles what we discovered in dealing with 
analysis. Without insight into the principle according to 
which the material can be unified, we do not really know 
what parts of the material are relevant and what are super- 
fluous and negligible. In consequence of this lack of insight, 
we may unguardedly omit something which is vital, or add 

2 Cf . W. MacDougall, Social Psychology, preface. 



224 SYNTHESIS 

something which is unnecessary or even misleading. In study- 
ing intelligence, for instance, what factors should be taken 
into account in our synthesis, and which elements should be 
omitted? Is ability in mathematical work, in logical tests, 
and generally in solving problems, to be estimated highly, 
while ability to reproduce strings of figures or nonsense-sylla- 
bles, and similar tests of rote memory, to be estimated as 
somewhat of a minus factor, if anything? And what are we 
to say of visual and auditory acuity, and in general of good 
powers of sense-perception? Is their possession a sign of 
intelligence, or not? Given, as data, answers to tests in all 
these fields, and the problem being to synthesise these data 
in such a way as to rank in order of intelligence the indi- 
viduals who have been tested, we clearly need insight into 
some principle which will tell us which tests are to be regarded 
as important, and which are to be entirely omitted, as of zero 
or minus value in estimating intelligence. Without such 
insight, we may blindly assign to sensory acuity a value equal 
to that assigned to the logical tests, or even assign a high 
value to the memory tests. In other words, we may include 
in our synthesis elements which are irrelevant or even contra- 
dictory, and thus may seriously vitiate our conclusions. In 
such cases we can learn to avoid an irrational and external 
completeness, and to approximate to a completeness which is 
reasonable, only after much experimentation with mental 
models, testing the tests themselves, until we find out with 
fair accuracy which tests constitute genuine elements, and 
which tests have a negligible value. 

So also, on the other hand, when evidence is scanty, and it 
is necessary to add elements in order to construct the required 
totality, as nearly as may be. Without insight into the prin- 
ciple in question, we shall not know what elements should be 
added, and may go seriously astray. In interpreting the con- 
duct of other persons, we have, as data to be synthesised, a 
number of observed actions. Our aim is, so to sum up these 
actions as to throw light upon the whole system of purposes 
and motives underlying a given individual's actions. Con- 
sider, for example, the character of the emperor Tiberius. On 
the evidence of the bare actions recorded in history, we should 
say, with certain critics, that he was a great administrator 
with poor social qualities, but of a character which, in the 
main, was highly valuable. Other critics, however, agree 



METHODS OF SCIENTIFIC SYNTHESIS 225 

with Tacitus in attributing to him a duplicity of purpose 
which is almost without parallel in the world's history. 3 His- 
torical reconstruction, in general, lends itself to additions 
here, and special emphases there, which may or may not be 
justified. How far they are scientifically correct, is a matter 
for careful weighing of the evidence. In cases, however, 
where the evidence still remains indecisive, suspension of 
judgment seems to be the only scientific course. 

In dealing, then, with natural phenomena — i. e., with data 
other than mental models — we seem unable to attain to full 
insight into a principle for unifying our data, and thus, in 
respect of both objectivity and completeness, our synthesis 
cannot be entirely successful. There is, however, no doubt 
that we can approximate to a synthesis wnich would be above 
reproach by using as mental models the most approved pat- 
terns. 

Methods of Scientific Synthesis (A) Mathematical. — The 
first and most universal of such patterns as are approved on 
the basis of experience, is the mathematical group of models. 
Whatever can be counted, can be added or synthesised, and if 
we can do nothing else, it is at least something if we can 
regard each of our data as approximately=l, 2, 3 ... , 
and can thus proceed to add them, or subject them to mathe- 
matical manipulation of some more advanced kind. A stu- 
dent's record in college, for instance, is expressed largely in 
terms of this kind of synthesis. In a given course there are 
(1) a number of papers, (2) a number of recitations, and (3) 
a final examination, as data. In most cases, the marking has 
been qualitative rather than quantitative. Recitations, for 
instance, are good, poor, or fair average. Papers are A, B, 
C. ... By assigning numerical values to these data in 
accordance with a definite rule, these elements can be added, 
weighted,^ and averaged in such a way as to satisfy the 
demands of an elementary synthesis. Such marking is 
admittedly never quite perfect, but the introduction of the 
mathematical type of synthesis is at least a beginning in the 
right direction, and is far more objective and complete than 
a mere arbitrary "general impression" would be. So also in 
the case of the intelligence tests mentioned above, and in gen- 

3 Cf . Furneaux. edition of Tacitus' Annals, and Boissier, Tacite. 

4 For what is meant by a "weighted" average, see A. L. Jones, 
Logic, p. 199. 



226 SYNTHESIS 

eral, it may be stated that in scientific constructions we have 
"science" in exact proportion as our constructions follow 
mathematical models. 

Such a synthesis in terms of mathematical models is always 
correct as far as it goes. In most cases, however, it must be 
admitted that it goes only a short way. It is preliminary to 
a more specific type of synthesis. Its function is, so to pre- 
pare the material, that we can manipulate our data more 
easily and with a certain approximation towards insight into 
the requisite principle of unification in the specific case. 
Thus, in estimating the state of prosperity of the country, if 
the data — e. g., market values of various staple commodities — 
have already been reduced to mathematical form and subjected 
to a manipulation which is mathematical and reduces them all 
to a common basis — we have already advanced a long way 
towards a synthesis which would satisfy economists. But in 
order to advance the whole way, we should have to go fur- 
ther and effect a synthesis which is specifically economical. 
The mathematician as such can handle data, but is without 
the specific insight into economical principles which is requi- 
site for effecting a synthesis which shall fall within the prov- 
ince of economics. So also in the case of physics, or psy- 
chology, or sociology. The mathematical synthesis is a nec- 
essary preliminary to further work, the final synthesis being 
effected by a physicist, psychologist, or sociologist. In the 
more preliminary stages of such sciences, the mathematical 
form of synthesis is almost the only one which is regarded as 
legitimate. But as such sciences progress further, the merely 
mathematical synthesis tends to be regarded as a method 
which is, indeed, universal and necessary, but is auxiliary 
and preliminary to the specific synthesis which it is the aim 
of the specific science in question to effect. 

(B) Causal. — A second mental pattern which, on the basis 
of experience, is thoroughly approved for scientific purposes, 
is the cause-and-effect model. Given as data, — as elements to 
be synthesised or put together in a way which will make 
sense — events, processes, and generally data with a temporal 
reference, it is found helpful to assume, as a mental pattern 
in terms of which they can be put together, a rule according 
to which one event or datum in time follows another. Mathe- 
matical models are employed as subsidiary methods, in the 
way explained above, but in dealing with events, the model 



METHODS OF SCIENTIFIC SYNTHESIS 227 

which exercises a controlling influence is the causal. The 
diagnosis of a case begins with an exact analysis and tabula- 
tion of the data in the form of symptoms. But, this analysis 
being completed, the next step is to put these data together in 
terms of some mental model which will throw light on the 
concrete situation which is the disease in question. The sore 
throat, high temperature, etc., are regarded not as mere units 
which can be added and subtracted, but as symptoms — i. e., 
as effects produced by some central cause, the disease whose 
nature is to be diagnosed. Certain phenomena of human 
growth are explained as caused by the direct activity of cer- 
tain glands, the rapid movement by which Dionaea Muscipula 
secures its prey is explained as caused by the series of changes 
initiated by the lever-like action of the contact-hairs, and in 
general, the adoption of this mental pattern has served to 
unify, in a way which makes sense, phenomena the most 
diverse in appearance, and data whose connection had for cen- 
turies remained an unsolved problem. The mathematical and 
causal types, then, are among the most universal and most 
valuable of the mental models by the aid of which we endeavor 
to make sense of the world in which we live. 

Validity of These Methods. — Mental patterns for explaining 
physical objects are seldom perfectly adequate in point of 
either objectivity or completeness. We have a bias in the 
direction of certain numbers, as when we imagine that every 
third wave, or every seventh or ninth, has the largest crest, 
or when we suppose that there are certain hidden rhythms in 
nature, which our poetic fancy can discover. So far as causal 
patterns are concerned, there is no human being but frequently 
believes causation to be at work when there is, in fact, noth- 
ing but hallucination. The belief in "ghosts" as causal factors 
in human affairs, in the influence upon our lives of "the stars 
which shone at our nativity," in our ability to propitiate the 
forces of nature by appropriate ceremonials — all such phe- 
nomena indicate a hasty and improper use of causal models,^ 
and there is no mental model which is not liable to such 
unmeaning or misleading usage. In themselves, then, such 
methods of synthesis are neither valid nor invalid. In respect 
of validity, the sole question which can be raised is, as to 
how we use them. To this question, as to the similar ques- 

5 Cf. Herbert Spencer, Data of Ethics, chapter iv. 



228 SYNTHESIS 

tion in respect of analytical methods, we can give only one 
answer. The sole test of such mental patterns is — Do they 
"work"? Do they actually help us towards acquiring insight 
into the principles in accordance with which the world in 
which we live seems to be constructed? Do they tend to 
diminish the margin of difference which separates the way 
in which we think of things as behaving from the way in 
which things are proved to behave, when considered more 
objectively? Do they, that is, lead towards a progressive 
insight into the workings of nature, and thus help us to under- 
stand and solve our concrete problems? If so, they are so far 
valid. If not, they are worthless, except as sources of amuse- 
ment — intellectual games which at best do no harm, but also 
do not bring us into touch with the objective worlds 

Summary. — So far, then, we have seen that synthesis is a 
preliminary portion of scientific method, and that it is of 
universal application. Its aim is, so to make use of the bonds 
of connection which hold data together, as to put together ele- 
ments in a way which is both objective and complete. This 
aim can be fully realised when thought is dealing with its 
own constructions, and in such cases only. In dealing with 
natural phenomena, we can only approximate to such a syn- 
thesis, by experimenting with mental models until we find one 
which seems to apply. Of such models, the most universally 
helpful are the mathematical and causal types. These can 
be regarded as valid so far as they are found to "work" — i. e„ 
to help us to escape from the vagaries of subjective imagin- 
ings, and to get into closer touch with the objective world. 
By such methods the way is opened for a synthesis which 
shall be progressively satisfactory. 



6 The reference here is to the "dialectical" method, by which one 
or more persons, by consulting their own tnoughts, would try to spin 
out of their own heads a philosophy of nature. The method originated 
with Plato (Of. the last half of the Timaeus), and is well developed 
in mediaeval science. But it is not unknown in the history of modern 
thought. The best known instances are Schelling's Naturphilosophie 
and certain of the speculations of Hegel. 



FOR FURTHER READING 

W.^Wundt, Logik, (3rd Edit.), Vol. II, pp. 8-11. 



EXERCISES 229 

EXERCISES 

Show what part is played by synthesis in dealing with the follow- 
ing cases: (1) In learning to use the typewriter. (2) If accidentally 
locked into a room, in getting out. (3) In finding the address of 
a friend the other side of town. (4) In estimating character in the 
case of strangers. (5) In laying out the plan for a small vegetable 
garden. (6) In keeping accounts. 



CHAPTER XXI 

ANALYSIS AND SYNTHESIS 

The Problem. — So far we have discussed analysis and syn- 
thesis in separation from one another, as though they were 
two sharply distinct and independent methods, and as though 
each could be applied by itself. In fact, they have seemed not 
merely independent, but even opposed. Analysis means tak- 
ing apart by loosening a bond of connection. Synthesis means 
putting together by introducing a bond of connection. And 
yet, there have been indications that perhaps our distinction 
was a little sharper in theory than is warranted by the actual 
use of scientific method in practise. It is doubtful whether 
any of the instances we have given can be regarded as pure 
cases of analysis or pure cases of synthesis. For example, in 
deciphering the message AAABB .... we certainly con- 
structed a complete cipher as part of our process of analysis. 
So also, in attempting to put together the elements hour, for, 
we, early . . . , we gave up one attempted synthesis after 
another, on the ground that they omitted certain of the data. 
But that certain of the data were being omitted could be 
known only by our analysing the totality which we were 
attempting to introduce, and then comparing its elements with 
the given elements. l That is to say, so far as our examples 
go, they seem to indicate a certain interconnection of analysis 
and synthesis. 

Again, if we compare the procedure, rather than the exam- 
ples, we find that analysis and synthesis agree in a number 
of essential points. Both proceed by the trial-and-error 
method, and by introducing mental models — models con- 
structed after a pattern which we can understand, or take 
to pieces and put together again. That is to say, the mental 
models which we use in both cases as a necessary and integral 
part of the method are themselves products of both analysis 
and synthesis — so that the analytical method uses models 
which are partly synthetical, and the synthetical method uses 
models which are partly analytical. 

230 



ANALYSIS AND SYNTHESIS 231 

Finally, both methods have fundamentally the same aim. 
In order to take apart, analysis must first discover, as nearly 
as may be, what it is which holds the elements together. In 
order to loosen the bond of connection, we must learn, if 
possible, what that bond is. So too with synthesis. In order 
to put together, we must have some unifying principle, some 
bond of connection, with which to go to work. Given ele- 
ments which are separate, they will not fall together of them- 
selves. Some organising principle must be introduced, and in 
order to put together, we must have insight into some such 
principle. The primary aim, then, of both methods appears 
to be identical. Whether we wish to analyse or to synthesise, 
in both cases the discovery of some unifying principle con- 
stitutes our primary aim. 

If we now put this evidence together, and realise that (1) 
our examples seem to employ both methods, (2) the mental 
models employed in both procedures are both analytical and 
synthetical, and (3) the primary aim of both methods is iden- 
tical, it seems more than doubtful whether the previous sug- 
gestion of the independence of the methods is not to be given 
up. It looks as though analysis and synthesis are thoroughly 
interdependent — as though they should be regarded, not as 
two methods, but rather as two correlative aspects of a sin- 
gle method of scientific investigation. The problem of the 
present chapter is to examine more closely into the relations 
of analysis and synthesis, in order \o discover whether there 
are two methods, separate and independent, or whether there 
is only a single method with two correlative and interdepend- 
ent aspects. 

Is Analysis Synthetical? (A) With Mind-Made Entities. — 
Let us begin by taking the analytical method and enquiring 
how far it essentially involves the use of methods which can 
properly be called synthetical. Suppose we find it necessary 
to take the lawn-mower to pieces. The ordinary procedure is 
to look it over, and to examine it somewhat as follows: — 
"These bolts are held in place by those nuts. If I loosen one, 
then this roller will fall out. If I loosen both, then I can 
remove the cutting blade also. To remove these revolving 
blades it will be necessary also to take off the nuts which 
hold that bar in place, etc., etc." That is to say, in our ordi- 
nary and natural procedure with machinery, we certainly look 
it over in order to form an idea as to how it is put together. 



232 ANALYSIS AND SYNTHESIS 

In this way we obtain an insight into its structure which can 
only be called synthetical. Even if we fail to look it over 
as a whole, and proceed merely by unscrewing every nut and 
screw in sight, and then by pulling out every bolt until the 
whole falls apart, we are using an insight which is synthetical. 
We act under the impression that it is screws and bolts which 
are holding the machine together — i. e., that it has been put 
together by these means. In dealing with machinery, then, 
with a view to taking it to pieces, an essential part of our 
analytical method appears to consist in considering how the 
machine has been put together — i. e., in considerations which 
are synthetical. 

Let us proceed to consider a second group of entities con- 
structed in accordance with a mental plan. We can analyse 
a triangle, for instance, by taking it apart into three straight 
lines. Is there any aspect of our method here which should 
be considered synthetical? It seems to resemble the machin- 
ery case just considered. We do not know how to go to work 
unless we understand the principle which holds the three 
angles together, unless, that is, we realise that three straight 
lines must meet so as to form angles in such a way that the 
whole is a closed figure. It is only when we understand what 
it is that holds the triangle together that we can take it apart 
in a way which is both objective and complete. 

If the above cases may be regarded as typical, we can state 
that, in analysing structures put together in accordance with 
a plan devised by the mind of man, — i. e., in cases where 
thought is dealing with itself — it is necessary for us to acquire 
insight into the principle of construction — a synthetical 
insight into the way in which such structures have been put 
together — in order to analyse in a way which shall be both 
objective and complete. That is to say, in such cases syn- 
thesis constitutes an integral portion of the analytical method. 

(B) With Natural Phenomena. — In endeavoring to analyse 
natural phenomena, our method is, as we have seen, to try 
out one mental model after another, with a view to finding out 
whether the structure of such mental models in any adequate 
way corresponds to the structure of the natural object which 
we are investigating. That is to say, we make guesses at the 
plan of structure of our object — we try to think out how it 
might have been put together, and then see whether our guess 
was correct, by trying to take the natural phenomena apart 



IS SYNTHESIS ANALYTICAL? 233 

in accordance with what we assume to be its structural plan. 
For example, in trying to understand the structure of the 
organ of hearing, the most widely accepted analysis is that 
which regards the basilar membrane as modelled on the struc- 
ture of the wires in a grand piano, and in fact an artificial 
model of just such a membrane has been made in accord- 
ance with this prescription. Other authorities try to analyse 
it along the lines of a telephone-like model.i So too in ana- 
lysing out the mechanical elements which enable a plant such 
as the bulrush or corn to withstand the pressure of the wind, 
it is usual to analyse such cases in terms of trusses and other 
engineering models. That is to say, in all such cases, we 
guess at the way in which the phenomenon in question may 
have been put together, as a necessary preliminary to taking 
it apart. Our conclusion, then, is, that whether we are dealing 
with the structures of thought or with the phenomena of 
nature, our analytical method contains, as an integral portion 
of its procedure, the construction of a model which is taken 
to represent the way in which the object-to-be-analysed has 
been put together. Analysis necessarily involves synthesis. 

Is Synthesis Analytical? (A) Mind-Made Entities. — Let us 
now proceed to study a little more closely the method of syn- 
thesis. We have before us as data a number of differently 
shaped pieces of wood, plus a frame — technically known as a 
"form-board." . Our problem is, to put these pieces of wood 
together in such a way that they will fit into the frame. We 
look over the pieces of wood, and then at the place into which 
they are to be fitted. We think: — "This piece could go here, 
these two pieces could be joined together so as to go there, and 
perhaps in this remaining space we could put the three or four 
remaining pieces." That is to say, we compare the space to 
be filled with the elements which are to fill it. On the one 
hand, we see that "these pieces could fill that space," and 
on the other, that "this remaining space could be filled by 
those three remaining pieces." In other words, when we 
attend more to the pieces and how they might be put together, 
our procedure is more synthetical. But when we attend more 
to the space and ask by what sort and number of pieces it 
could be filled, our procedure is more analytical. We pro- 
ceed in this doubte way, and there is always some occasion for 
comparing (1) what we want to do and (2) the means at our 
disposal. When we make such a comparison, we necessarily 

i Cf. W. B. Pillsbury, Fundamentals of Psychology, pp. 169-170. 



234 ANALYSIS AND SYNTHESIS 

analyse what we want to do, and see how the elements yielded 
by this analysis compare with the materials which have been 
put at our disposal. "If this piece were only a little shorter, 
it could be fitted in." That is to say, in putting together 
mechanical apparatus, our synthetical method includes an 
analysis of the totality which we wish to construct. 

So too in other cases of the same general type. In solv- 
ing a problem by means of simultaneous equations, we start 
by stating our data in algebraical form. "Let x= this, and 
let 2/=that. . . . " But when we come to the work of 
synthesising our x J s and y's so as to represent in equational 
form the conditions which form our data, there is no doubt 
that we proceed in the two-fold way which we have noted 
above. We keep one eye upon the data, and the other upon 
the equational form in which we are trying to express those 
data. In the whole process of trial and error which culmi- 
nates in the requisite equations, we are suggesting one equa- 
tional content after another and rejecting it, if its elements 
differ from the elements which form our data, until in the 
end we find one which seems to satisfy all the conditions. 
That is to say, we analyse each suggested equational content 
into its elements in order to compare them with our data and 
see how far they coincide. So also if we are called upon to 
invent a plan which will satisfy certain given conditions, and 
provide us with a complete solution to some examination 
problem in ethics or economics. We try one suggested plan 
after another, analysing it in order to discover whether the 
conditions which it will really satisfy are the same as the 
conditions given in the examination paper. In other words, 
here also our synthetical method includes an analysis of the 
totality which we wish to construct, and if these instances 
may be regarded as typical, we can state that in dealing with 
mind-made entities we always, as an integral portion of our 
synthetical method, analyse the totality which we are attempt- 
ing to construct. In such cases, then, synthesis necessarily 
involves analysis. 

(B) With Natural Phenomena. — Where thought is not con- 
fined to its own constructions, but is attempting to get into 
touch with natural phenomena, what is our synthetical pro- 
cedure? We try, as we have already seen, to put together our 
data in terms of some mental model, — primarily of a mathe- 
matical or causal type — which is especially designed to fit the 



IS SYNTHESIS ANALYTICAL? 235 

concrete situation as nearly as possible. In order to discover 
whether it does reasonably fulfil the requirements of the sit- 
uation, it is, of course, necessary to analyse the mental model, 
and compare the elements into which we dissect it, with the 
elements which constitute our concrete data. For example, 
given as data the various species of animals, and the problem 
being to put them together in such a way as to obtain insight 
into the principle of specification and thus make sense of the 
infinite variety of nature — how have men proceeded? The 
older theory, that each species had been especially created, 
resolved the whole question into "the inscrutable will of the 
Creator," and thus, in effect, gave up the problem. The more 
modern attempts at a solution in terms of the evolutionist 
hypothesis very definitely consist in introducing some mental 
model of what evolution is, and what results it would pro- 
duce, if analysed carefully. These results of theoretical anal- 
ysis are then carefully compared with the empirical facts, and 
this is the regular scientific method used in dealing with 
scientific phenomena. 2 In other words, in dealing with either 
mind-made entities or the phenomena studied in natural 
science, our attempts at synthesis always contain, as an inte- 
gral portion of their constructive nature, some degree of anal- 
ysis of the totalities which we wish to construct. Synthesis 
always involves analysis. 

Summary. — So far, our examination has borne out the sug- 
gestions with which we started. Analysis involves synthesis, 
and synthesis involves analysis. There is thus no sharp dis- 
tinction to be drawn. There are not two independent meth- 
ods, each of which can be applied singly and separately. Anal- 
ysis and synthesis are thoroughly interdependent, and consti- 
tute a single method. There is a single analytic-synthetic 
method, whose function is to enable us to obtain insight into 
the world in which we live by means of taking apart and put- 
ting together again phenomena in which we are interested. It 
is by constructing experimental models and trying them out 
in relation to the actual phenomena, that our mental grasp of 
the world grows, and it is in this feature — the construction of 
mental models for purposes of experimentation — that we 
should look for the chief characteristic of the method. For 
this is what both analysis and synthesis have in common. (1) 
In respect of ultimate aim — to understand the world in which 

2 Cf. Huxley's lecture on The Demonstrative Evidence of Evolution, 
quoted in A. L. Jones, Logic, pp. 287-300. 



236 ANALYSIS AND SYNTHESIS 

we live, — (2) in respect of proximate aim — to grasp the par- 
ticular principle of connection which holds together a system 
of elements or concrete situation in which we are interested, 
— and (3) in respect of method — the construction of mental 
models which can be taken apart and put together again — 
analysis and synthesis are indistinguishable, and are so far 
to be regarded as identical. 

Differences Between Analysis and Synthesis. — And yet, we 
must be careful to avoid a too hasty conclusion. Perhaps the 
view which we are taking may turn out to be too one-sided. 
Analysis and synthesis can hardly be regarded as wholly 
identical. Analysis has seemed more preliminary, more rudi- 
mentary, less flexible, less able to take account of rational con- 
siderations. It is apparently tied down to the given material, 
and appears to be without power of discrimination, either in 
respect of omission of what is irrelevant, or in the way of 
addition if some further element is plainly demanded to com- 
plete a datum which is fragmentary. Synthesis, on the other 
hand, has seemed to be more a completing of the investigatory 
process, a summing up of the results of the inquiry, and a 
final reconstruction of the principles which have been studied. 
It appears largely to come after the work of abstraction and 
determination, and thus to be more discriminative than mere 
analysis. It can apparently omit what is not required, improve 
upon its data in the way of economy and efficiency, and even, 
to a large extent, supplement its data by completing curves, 
filling up gaps, extending applications. It seems of greater 
efficacy in the positive or more constructive work of organisa- 
tion, and generally to be a more advanced and final repre- 
sentative of what we mean by scientific method. 

Again, analysis appears to be easier than synthesis. More 
people can take a machine to pieces than can put it together 
again. Nearly every recruit can follow instructions so far 
as taking his rifle apart is concerned. But when it comes 
to putting it together again, a large percentage of the new 
men are driven to seek assistance from the sergeants. So 
too any boy can take a clock to pieces. But when it comes to 
putting it together again, it has to go back to the clock-maker, 
unless the boy has a quite exceptional mechanical ingenuity. 
So too many students can follow a lecture in class or read an 
assignment at home, and can take it apart well enough. But 
when it comes to putting together again what they thus 



APPARENT DIFFERENCES 237 

studied, they frequently come upon unsuspected difficulties. It 
looks, then, as though it must be one thing to take apart, and 
another and more difficult thing to put together. 

(A) Apparent Starting-Point. — Let us consider, then, some- 
what more closely the apparent difference^ between analysis 
and synthesis. In the first place they differ in respect of their 
apparent starting-point. The datum for analysis appears to 
be a complex totality, and the problem is, to take this to 
pieces. More exactly, the problem is, to find out what are the 

pieces. In the case of the cipher AAABB , for 

instance, we might suppose the elements in question to be com- 
binations of A, combinations of B, or even simply and ulti- 
mately A and B. But as these suppositions are false, we 
should in this way be analysing, not the cipher, which is our 
real datum, but certain aspects of its mechanism of expres- 
sion. In fact, the cipher is expressed in a way which is 
intended to conceal its real elements from all but the ini- 
tiated. It is not certain what is the datum before the analysis 
has proceeded some little distance. The real datum is a sig- 
nificant message expressed in a form intended to conceal its 
real nature and mislead the analytical investigator, and it is 
this datum which analysis has to take apart. It is the sig- 
nificance which holds the elements together, and it is only 
when our thought has penetrated some way into this signifi- 
cance — i. e., only when we have apprehended what the datum 
is, that we can avoid being misled, and can pick out the gen- 
uine elements. For analysis, then, the apparent datum is a 
(rational) complex, the product of synthesis. 

For synthesis, on the other hand, the apparent starting- 
point is a number of disconnected elements, which have already 
been analysed out, such as N, 0, T, H, S, A, G, W, 7, N, and 
the problem is, to put these together in such a way that they 
make sense. More exactly, the problem is, to reconstruct the 
original totality, to discover what was the rational principle 
which united into a connected and nieaningful form, these 
elements which are apparently given as disconnected. Here 
again, however, there is a difference between the apparent 
and the real datum. It is not at first apparent what the 
genuine datum is. It is not just a group of letters, but it is 
ten very definite letters which are given as elements which 
together constitute a totality, i. e., as elements which can be 
rationally connected so as to spell out a single name, elements 



238 ANALYSIS AND SYNTHESIS 

which are significant, and it is only so far as our thought 
penetrates into their significance — the meaningful principle 
which connects them even in this apparently disconnected 
form — that we can escape misleading associations, and can 
hope to discover tfye totality in question. For synthesis, then, 
the apparent datum is a (rational) group of elements, the 
product of analysis. 

Thus we see, that while both analysis and synthesis are 
dealing with a datum which in an ultimate sense is one and 
the same — viz., a significant totality whose significance is par- 
tially concealed beneath its outward form — yet this ultimate 
datum is given in two different-appearing aspects. For anal- 
ysis, the aspect which is prominent is the totality or com- 
plex unity. For synthesis, the aspect which is prominent is 
the scattered, severed, plural, disconnected form of the data. 
Thus we see that, while both methods are ultimately dealing 
with one and the same reality, the aspects of this datum 
which are most apparent, differ for analysis and synthesis. 

(B) Apparent Conclusion. — In the second place, the conclu- 
sion to which the use of these methods leads, seems to differ 
according as we emphasise the analytical or the synthetical 
aspect. Analysis starts with a totality and concludes with a 
disconnected group of elements, with elements whose plurality 
and distinct nature is sharply emphasised. And yet, is this 
the whole conclusion? It is certainly the apparent conclusion, 
but, if we examine further, we find that we think of our ele- 
ments not entirely as disconnected, but partly also as inter- 
connected in the totality. In analysing an argument, for 
instance, we tend to group its different steps as (1), (2), (3), 
. . . , thus emphasising, not merely their distinct charac- 
ter, but also the fact that they are each and all steps in one 
and the same argument. That is to say, the elements with 
which we conclude are not just elements-in-general, but defi- 
nite elements, elements of the particular complex which fur- 
nished our starting-point. The genuine conclusion, then, is 
not so much a group of elements as the real nature of our 
datum. Our conclusion is an analysed complex — a totality 
broken up into its elements and held over against those ele- 
ments by the mind, in the general form x=(a-\-b+c . . .). 
In the same way the real conclusion of our analysis of the 
bundle is not a number of sticks, but the very same sticks 
which constituted the bundle, plus the now untied rope by 



APPARENT DIFFERENCES 239 

which they had been held together. There is, then, a sharp 
distinction between the genuine conclusion and the conclusion 
which is apparent. The apparent conclusion of analysis is a 
number of disconnected elements. 

What is the conclusion of the operation of synthesis? We 
start with elements and we end — at least apparently — with a 
totality. At least it is the unity, significance, and complex 
individuality of our conclusion which are emphasised. With an 
old pack of cards, if we use a careful method of inter-weav- 
ing, we can create a card-house which will not fall apart, and 
which will be the admiration of children. The whole empha- 
sis is on the unity, strength, and consistency of the totality. 
The whole emphasis? Let us examine further. Is not the 
emphasis always an affair of contrasts? Surely it is as con- 
trasted with such beginnings that we admire the conclusion. 
Out of such elements to constitute such a totality — that is 
rather the idea in our minds as we contemplate the result. 
The genuine conclusion, then, as not the bare result, but 
rather the resultant-of-a-method-applied-to-these-definite-data. 
Our conclusion is no mere x, but an x which has been con- 
structed out of (a+t + c . . . ). That is to say, while 
superficially it might seem as though the conclusion of our 
synthetic process was the bare totality, the genuine conclusion 
is the totality-as-constructed-out-of-the-data. Expressed in a 
general formula, it is (a+b-\-c .... )—x. 

Thus we see that the genuine conclusion at which both 
analysis and synthesis arrive is the same. Both are equally 
dealing with an organic unity, a totality or individuality which 
has two aspects. We can regard it as a one-in-many, as 
a unity which has also an aspect of plurality, as a totality 
which is composed of elements. Or on the other hand we 
can regard it as a many-in-one, as a plurality which has also 
an aspect of unity, as elements which together make up a 
totality. We can regard it either in the form x = (a -\-b + c 
. . . ), or in the form (a+b+c . . . )=x. The reality 
underlying both aspects is one and the same, and it is with 
this reality that our scientific method is trying to bring us 
in touch. But analysis aims more at expressing this reality 
in the one form, and synthesis at expressing it in the other. 
So far as we are dealing with conclusions which thus appear 
different, we can distinguish analysis from synthesis. But 
so far as these are aspects of an underlying reality which is 



240 ANALYSIS AND SYNTHESIS 

one and the same, analysis and synthesis do not differ in 
any fundamental logical respect. 

(C) Apparent Method. — In the second place, the method we 
use seems to differ according as we emphasise its analytical 
or its synthetical aspect. So far as we are conscious of our 
method, we believe that in analysis we are taking to pieces. 
The recruit is apparently taking his rifle apart — and to a 
mind which is satisfied with appearances, with aspects which 
are prominent, that is all that he is doing. And yet, if we 
look a little further, it is not difficult to realise that he is doing 
more than that. The whole point of teaching a recruit to take 
his rifle apart is, not merely that he shall clean his weapon, 
but that he shall acquire an insight into its mechanism which 
he could acquire in no other way. He takes it apart in 
order to see how it is put together, and how it works. The 
method has, in fact, synthetical as well as analytical aspects. 
The true method of analysis, then, is analysis plus synthesis, 
usually in terms of some mental model which has both aspects. 
The apparent method, however, may be regarded as merely 
analytical, merely taking to pieces. 

So too in synthesis. So far as we are conscious of our 
method, we believe that in synthesis we are putting together 
and constructing. The chief stress is on the positive, build- 
ing-up characteristic of the method. So far as appearances 
go, we are putting together the pieces of wood so that they 
will fit into the space in the form-board, and if we are satis- 
fied with the appearances which are prominent, this — the 
putting together — seems to be all. And yet, if we look a 
little more closely, it is not difficult to realise that at the 
same time as we are putting together the pieces of wood, we 
are analysing the space which we expect to fill with them. 
The true method is both synthetical and analytical. We 
analyse the totality which we wish to construct, as well as 
synthesising the means at our disposal for purposes of con- 
struction. The apparent method, however, may be treated 
as merely synthetical, merely putting together. 

Thus we see that, so far as the real method is concerned, it 
is the same, whether we call it analytical or synthetical. In 
both cases the method consists in the analysis of a totality 
into its elements and the synthesis of elements into their 
totality. The logical relation involves both the relation of 
parts to their whole, and of a whole to its parts, and this 



IS SYNTHESIS MORE ADVANCED? 241 

relation is fundamentally the same for both analysis and 
synthesis. The recruit who puts his rifle together is at the 
same time learning to take it apart, just as in taking it 
apart he is at the same time learning how to put it together. 
In both cases, what he is studying is the same — the relation 
of the whole rifle to its parts, and of the parts to the whole 
rifle. He is learning how the rifle works, and the analytical 
and synthetical methods are two ways of doing the same 
thing. So far, then, they are not to be distinguished. There 
is only one method. But it has two aspects, either of which 
can be made prominent. According as the one or the other 
aspect is the more prominent, we can distinguish the taking- 
apart aspect from the putting together aspect. In respect, then, 
of the method apparently employed, we can distinguish 
analysis from synthesis. 

Is Synthesis a More Advanced Method? — In the light of 
these considerations, we should note that it is only when 
speaking of the "apparent" methods, that we can regard 
synthesis as more advanced and analysis as more preliminary. 
For example, analysis is not really confined to its data, but 
in virtue of the synthesis inherent in its method, can omit 
or supplement, as far as is desirable. Thus, in analysing the 
message "The supply of game for London is steadily going 
up," if we wish to discover the elements which are really 
elements of the concealed message, nothing whatever can be 
done with "supply," "of," "for," "London," etc., These are 
just words added in order to mislead, and form no part of 
the genuine message. It is necessary to construct a mental 
model for message-sending which shall emphasise every third 
word only, filling up the intervals with words which seem to 
make sense but really conceal the meaning which is intended. 
This mental model, which is constructed by synthesis, is 
however the principle of the cipher, and thus an analysis 
which really analyses the cipher — the genuine datum — will 
be an analysis which omits such words as "supply," "of," 
etc., and picks out the first, fourth, seventh, etc., words as 
genuine elements. Analysis is thus not restricted to its 
apparent datum, but can transcend this either by way of 
omission, or by way of completion, if some element is clearly 
demanded by the context which our synthetic mental model 
gives us. At the same time, analysis is restricted to the true 
datum. But then, the true datum is the same for synthesis 



242 ANALYSIS AND SYNTHESIS 

also. Synthesis transcends only the apparent datum, and is 
rigidly bound by the true datum. Thus, in assembling an 
automobile from a miscellaneous collection of elements, only 
those are selected which really belong together, which can 
be utilised in assembling a single machine. The others are 
rejected, as forming no part of the true totality. In this 
way, then, we see that synthesis is not more advanced than 
analysis. Both aspects of the analytic-synthetic method stand 
on the same level. 

Summary. — So far, then, we realise that from a standpoint 
which is satisfied with appearance, analysis and synthesis can 
be sharply distinguished in respect of starting-point, conclu- 
sion, and method. But if we persist in looking beneath appear- 
ances, we must reinforce our earlier conclusions, and believe 
that there is only one method. Our final conclusion, then, is 
that strictly speaking there is only one fundamental method, 
the analytic-synthetic method, but that this method has two 
interdependent and correlative aspects, of which the one 
consists in taking apart, and the other in putting together, 
and that for practical purposes it may be advisable to empha- 
sise now one, now the other, of these aspects. For strict 
logical theory, however, it is essential to realise that, whether 
we wish to analyse or to put together, we are employing a 
single fundamental method, which aims at understanding the 
world in terms of the part-whole relation, the mental model 
which gives us the structure of organisation. Analysis and 
synthesis are, then, the two correlative aspects of a method 
which endeavors to understand the world in which we live 
as a rationally organised whole. 

FOR FURTHER READING 

F. H. Bradley, Principles of Logic, Bk. Ill, Part I, chapter vl. 
H. Lrotze, Logic, Bk. III. Introduction, pp. 406-409. 

EXERCISES 

Show the inter-relation of analysis and synthesis in dealing with 
the following cases: (1) In learning to sing or to play on a musical 
Instrument. (2) In choosing a new suit. (3) In escaping from the 
top floor of a building in case of fire. (4) In considering whether 
to insure one's life or not. (5) In translating from a foreign lan- 
guage. 6) In estimating one's probable expenditure for the next 
month or year. 



CHAPTER XXII 
ABSTRACTION 

"One thing at a time" is the motto of abstraction. By its 
aid we can consider an acquaintance from the sole standpoint 
of personal appearance, or commercial standing, or political 
leanings, or church membership. We can select friends on 
the basis of golf-playing, to the total neglect of other charac- 
teristics, or of interest in music, art, public service, or what 
not. In every day life, its use is sometimes helpful, some- 
times harmful. But for purposes of scientific investigation 
its importance is vital. Unless we could deal with one aspect 
at one time, any subject at all complex would be hopelessly 
beyond our understanding. But when we divide it up, and 
consider a single aspect at a time, something can be done. It 
is by the aid of abstraction that the division of labor is pos- 
sible, one worker tackling one part of a task, and another 
concentrating his energies upon another part, and it is by 
this division of labor that complex and highly developed 
results are possible, in commercial life or in science. Abstrac- 
tion is thus one of the watchwords of scientific management. 
It is one of the chief elements in organisation. 

Nature of Abstraction. — Abstraction is no preliminary 
method. It presupposes both analysis and synthesis, and may 
be regarded as a further development ef the analytic-synthetic 
method. Its starting-point is no concrete situation given in 
nature, but a situation which has already been analysed out 
into a number of different factors. Let the starting-point be 
symbolised by x = (a + o + c). Abstraction proceeds by tak- 
ing out of its context any one of these elements, a or & or c, 
and deliberately neglecting the others. Abstraction means 
talcing out of its context. It is thus a highly artificial process 
and leads to a highly artificial result. When we say that a 
statement is "abstract/' we usually mean that it is artificial 
and cut off from the actual flow of experience as experience 
is given to us. 

Abstraction, then, is the exclusive concentration of atten- 

243 



244 ABSTRACTION 

tion upon some one element of a complex whole. Its nature 
is thus negative as well as positive. Negatively regarded, it 
excludes rigidly every suggestion of natural context. The 
statistician considers people merely as so many numbers in 
the "population." The politician considers them merely as 
so many potential votes for or against himself or his party. 
Both exclude from consideration the rich professional and 
domestic interests and activities of the individuals in question. 
So too a salesman's chief business is to "get orders," an 
artist's chief business is to paint pictures, etc. Abstraction 
thus excludes breadth of vision and confines itself to a rigidly 
narrow outlook. On the other hand, however, this narrow- 
ness has certain positive merits. The outlook of abstraction 
is intensive, and makes for efficiency. It not only takes 
away, but it gives something new. When we abstract, we do 
not merely cut off an element from its context. It is, of 
course, cut off, but the mind proceeds to fix it, to give it a 
certain self-subsistence, to give it an independent nature and 
unity of its own — which, amongst other things, can be named. 
"Whiteness," "softness," "depth," ticklishness," "individual- 
ity," etc., are abstract qualities, qualities taken out of their 
original contexts and endowed with a certain kind of being 
peculiar to themselves. The entities to which our scientific 
concepts and laws in the first instance apply, are one and all 
of this abstract and artificial, half mind-made kind. They 
are taken out of their natural contexts in experience and are 
endowed with a new nature and unity. The nature of abstrac- 
tion, then, is to take out of its context a single element, or 
group of elements, and to endow this entity with an artificial 
kind of self-subsistent being. 

Aim of Abstraction: (A) Objectivity. — What precisely is 
our aim or intention in abstracting aspects or elements from 
their contexts? In the first place, we aim at objectivity. The 
whole point of abstracting is to bring ourselves into still 
closer contact with objective reality than is possible by the 
use of analysis and synthesis alone. It is because we are 
helpless in the face of nature taken as a whole, that we 
endeavor to proceed piecemeal, taking one small problem at a 
time and breaking up our analysed totality into elements 
which we can examine separately, and thus proceed gradually 
to understand the whole. If we wish, for instance, to study 



AIM OF ABSTRACTION 245 

memory, we immediately discover that the subject is far too 
wide to be grasped all at once. Accordingly, we narrow it 
down, first to mechanical or rote memory, then still further, 
until finally we begin to direct our experimental attention 
upon some such problem as "How many repetitions does it 
take to learn a series of twelve nonsense-syllables"? or "What 
part does such and such a rhythm play in helping us to learn 
such a series"? or "Does learning a series in the forward 
direction help or hinder learning it in the reverse direction"? 
It is only after solving an enormous number of such narrow 
and special problems that we can begin to approach the more 
general questions connected with remembering. That is to 
say, abstraction brings us into closer and more intimate con- 
tact with the subject which we wish to study. So too if we 
wish to acquire mastery over some musical instrument, we 
can, it is true, attain to a certain level of general accomplish- 
ment by just playing anything and everything in which we 
are interested. But there comes a time when we have to 
choose between remaining at this low level, and giving up 
our interesting show-pieces in favor of technical studies, each 
of which is designed to assist us in acquiring some small 
and special point of execution. We practise a school of 
velocity, an art of finger-dexterity, a volume of octave-studies, 
etc., and this concentration of attention upon one point at a 
time helps us to work our way into the subject itself, to become 
acquainted with its difficulties and its peculiarities. But for 
the fact that our scientific insight and artistic execution sens- 
ibly improve by the use of this method, we should never 
abstract and substitute a study which is dull and dry for 
the living reality. If it were not that we actually feel our 
way better and more surely into the subject studied by this 
method, we should never apply ourselves to mathematics, 
grammar, or logic, but should be like the young Deities of 
romance, knowing all things by the sheer might of our 
minds. Our primary aim, then, in abstracting, is objectivity. 
(B) Completeness. — A secondary aim, which is always 
before us when we abstract, is a certain kind of complete- 
ness. At first sight it might seem as though abstraction 
explicitly avoided completeness, because it aims at fragmen- 
tariness, at producing incompleteness, at isolating some ele- 
ment and separating it from the context which completes it. 
This is, indeed, true, but is not quite what is meant. It is 



246 ABSTRACTION 

at the complete isolation of this element that abstraction 
aims. Negatively, the context or contexts in which such an 
element is found must be stripped off and excluded from con- 
sideration, and this is to be carried through completely. Posi- 
tively, the element which is thus isolated is to be fully repre- 
sented in its own nature, in complete independence of its 
original context or contexts. The element thus abstracted 
is to be understood and studied in its complete nature, so far 
as this is possible. This means in practise, that the element 
in question must be abstracted from a variety of different con- 
texts, in order that we may escape from one-sidedness and may 
take a complete view of the element which we are abstracting. 
Thus, in studying the question as to whether Yellow is "sim- 
ple" like red, green, and blue, or "composite" like purple, it 
is usual to experiment with sun-light, with gas-light, with 
electric light, etc. — i. e., with a Yellow drawn from as great 
a variety of sources as possible. So too in studying in what 
sense an author uses a particular expression — e. g., what 
Aristotle understands by "nature," or Kant by "conscious- 
ness-in-general" — it is usual to put together all the instances, 
taken from a wide range of contexts, in order to avoid one- 
sided errors and to attain to a complete view. 

How Far Realisable? (A) With Mind-Made Entities. — How 
far can this aim be realised? That is to say, how far can 
we, while completely singling out and separating from its con- 
text some aspect of a larger whole, attain to objectivity? Let 
us see. In dealing with a complicated electrical machine 
which refuses to work, we try to discover what is wrong by 
the method of abstraction. We single out for special test- 
ing one contact after another, until we find where it is that 
the current is broken. Each case of singling out is here a 
single abstraction, and our method is certainly objective. For 
it deals with special elements which analysis discovers in 
the object itself. The contacts are parts of the machine, and 
they are the parts which it is important to investigate. 
Whether our abstraction is complete or not, depends upon 
the way in which we deal with each individual contact. It 
is certainly possible to isolate it from the rest of the machine 
and to test it completely with full reference to its objective 
nature. If this case may be regarded as typical, then, we 
can state that in dealing with machines our abstraction can 
be both objective and complete. 



AIM OF ABSTRACTION 247 

Let us consider another example. In looking over a system 
of shorthand, or in estimating the claims of some new arti- 
ficial language, it is possible to concentrate attention exclu- 
sively upon some particular feature — e. g., with a view to 
improving and simplifying it. In all such cases, i. e., where 
thought is dealing with its own constructions, our abstraction 
can be objective — for it is directed upon some particular sign 
in shorthand, or upon some particular rule in the artificial 
language, etc. Whether it is complete or not, appears also 
to be in our power. It is merely a question of studying our 
subject carefully, avoiding misleading associations and con- 
centrating our attention upon what is before us. If these 
instances are typical, we can say that, in dealing with mind- 
made entities, our abstraction can realise its aim in point 
of objectivity and completeness. 

(B) With Natural Phenomena. — As has been already stated, 
abstraction is no preliminary method, but starts with a datum 
which has already been analysed, and proceeds to concentrate 
attention upon some one of the elements revealed by analysis. 
It is therefore with a mental model, rather than with the 
natural phenomenon itself, that we are more immediately 
concerned in abstraction. But even here, the chief value of 
the method is that it brings us into closer connection with 
the objective facts than would be possible without its aid. 
Let us consider an example. J. Chr. Wolff's Psychologia 
Empirica is a product of analysis and synthesis. If, however, 
we wish to test its objective significance, we concentrate 
attention upon some special "proposition" or group of "propo- 
sitions." Let us take one. Wolff asserts that the laws of 
waking life are diametrically opposed to the laws of dream- 
life, so that, whereas waking life is rational, deliberate, etc., 
the dream-life is irrational, and does not admit of delibera- 
tion, choice, etc. We test this case by bringing special experi- 
ments to bear. We test the laws of association — they seem 
to be fundamentally the same in both cases. We make exper- 
iments upon reasoning. These also give similar results, for 
many dreamers solve mathematical problems. We test delib- 
eration and choice. Many dreamers deliberate, and many 
dreamers exercise choice and volition. After making a large 
number of experiments of this general type, we find ourselves 
much closer to the objective facts than we were by reacting 
and accepting the system of Wolff. In dealing with natural 



248 ABSTRACTION 

phenomena, it is precisely by such specialised observations and 
experiments that we bring ourselves into closer relation to 
the objective facts. That we can attain to complete objectiv- 
ity in dealing with such facts, is not claimed. But that we 
can improve our objective grasp upon the workings of nature, 
and can improve it indefinitely — i. e., progressively and with- 
out limit — by the help of abstraction, there can be no doubt. 

Completeness in any final sense, when we are dealing with 
natural phenomena, is perhaps out of the question. We col- 
lect as great a variety of instances of the aspect of our phe- 
nomenon under study, as is possible for us, and endeavor, by 
comparing these with one another, to escape the danger of 
one-sidedness and to make our abstraction complete. But 
that we can do more than approximate to this aim, appears 
improbable. For example, in psychology, we try to experi- 
ment upon attention, or memory or reasoning, and upon some 
special point in one of these fields, to the complete exclusion 
of every point other than the one we wish to study. This 
complete exclusion cannot however, as a rule be accom- 
plished, and thus we have to content ourselves with taking a 
number of instances of our phenomenon from different angles 
of approach, and, by putting these together, to eliminate the 
elements peculiar to each case and thus obtain something 
like a concentrated, intensive view of the common elements 
present in each case — elements which are more directly con- 
nected with the problem under study. By studying the phe- 
nomenon now in this context, now in that, we are enabled to 
loosen somewhat its connections with any particular context, 
and gradually to frame an idea of it apart from the contexts 
in which we have experienced it. This is .an indirect method 
of abstraction, and is found helpful in direct proportion to 
the variety of the instances compared. But a complete 
abstraction is hardly attainable by such means. However, by 
concentrating our attention, as far as possible, upon a single 
aspect at a time — as in some of our more specialised intelli- 
gence tests — it is possible to improve our methods of experi- 
mentation, and gradually to revise the generally adopted 
mental models with which work is done in such fields. Abstrac- 
tion, then, though not perfectly complete, is a method which 
leads to progressive improvement in dealing with natural 
phenomena, in respect of objectivity. 

Types of Abstraction (A) Isolation. — So far we have seen 



TYPES OF ABSTRACTION 249 

that abstraction is a method of separating from its context 
some aspect of a phenomenon in which we are interested, and 
it might seem as though abstraction, as such, must be a 
method of isolation. It is usual, however, to distinguish two 
main types, (1) isolation, and (2) generalisation. When a 
machine such as a telephone refuses to work, the repairer 
takes one fuse at a time, and proceeds from one contact to 
the next, testing each one until he discovers the cause of the 
difficulty in question. .That is to say, he proceeds very def- 
initely by a method of isolation. He takes each contact by 
itself, and tests it to see whether it is in working order, 
without any reference to the rest of the mechanism. That 
is an example of the method of isolating abstraction. So too, if 
in trying to play a difficult study a music student finds there 
is some point of technique which is beyond his immediate 
powers, he practises that particular point of technique — e. g., 
the trill or mordent — by means of specialised studies until he 
has mastered it. It is by specialisation, or by isolating 
abstraction, that he overcomes his difficulties. This instance 
differs slightly from the telephone case. In dealing with 
machinery, we isolate a single instance, and are satisfied 
with that. In practising so as to learn to execute the trill, 
we specialise on that general kind of finger-movement, and 
practise as great a variety of trill-studies as possible, so as 
to be able to play the trill in whatever kind of context we 
may happen to meet it. That is to say, in this type of case 
we isolate by taking as many varieties of the phenomenon 
under study as possible. There is, however, no difference in 
principle between the two types of instance. All isolation 
is with a view to specialised study, and both varieties of 
isolation illustrate the principle of abstraction. 

(B) Generalisation. — Generalisation is not, in principle, 
different from isolating abstraction. But from a superficial 
standpoint it certainly appears different. For instance, it 
seems to lead to a different kind of result. Most empirical 
laws, e. g., are generalisations from a number of experiences. 
We find that graduate students in psychology can, as a gen- 
eral rule, learn a series of twelve nonsense-syllables in from 
seven to nine repetitions. We put together the results of 
several distinct observations based upon certain further 
experiments of this general type, and gradually construct a 
memory curve, a learning curve, a practise curve, etc. Each 



250 ABSTRACTION 

of these is a generalisation on the basis of repeated experi- 
ence. Thus we see that not only the practical wisdom which 
accumulated experience of men and things brings with it, 
but also most of the concepts and laws of empirical science, 
are products of generalising abstraction. We arrive at such 
generalisations by isolating, so far as we can, instances of 
the special phenomenon under study, in order to eliminate 
what is irrelevant to our purposes, and thus from a variety of 
instances extract the composite result which we call a gen- 
eralisation. Like the more complex cases of isolation, gen- 
eralisations are thus products of an abstraction which works 
by isolating special aspects of phenomena in which we are 
interested. 

Validity of These Methods. — There is nothing sacrosanct 
about abstraction in any of its forms. Isolation always has 
its dangers. In separating some particular aspect from its 
context, it is peculiarly easy to omit something vital or to 
add something which is irrelevant. Too much attention to 
detail, e. g., in literature, prevents our appreciating the 
whole, and it is often that we fail to see the wood because 
we direct our attention too exclusively upon particular trees. 
So too generalisations are often hasty and erroneous, the pro- 
ducts, as we say, of a "vicious" abstraction. Thus, in what 
is known as "Faculty" psychology — which represents a gen- 
eral tendency, rather than any definite school — we regard our 
minds as consisting somehow of a number of distinct "facul- 
ties," such as Memory, Reasoning, Will, Emotion, Sensation, 
e£c.i That is to say, we come to regard what we have taken 
apart into elements as though in itself it consisted of a num- 
ber of distinct elements. Such "hypostatisation," as it is 
called, is the peculiar danger of abstraction, and is a com- 
mon source of error in all the mental sciences. 

Abstraction, then, is sometimes invalid. On what does its 
validity, when it is valid, depend? It is valid only so far as 
it leads to progress in obtaining insight into the workings 
of the phenomena in which we are interested. So far as it 
leads to a definite advance in scientific knowledge, it is valid. 
But it must always be remembered that what we separate 
for purposes of special experimentation, is given together 

i Cf. Locke's Essay on Human Understanding, Bk. II, chapter xxi, 
sects. 17-20, and G. F. Stout, Manual of Psychology, 1899, Bk. I, chap- 
ter ill. 



EXERCISES 251 

with various other elements, and that it may be fatal to 
regard as separate in itself what we have found useful for our 
special purposes to regard as so far separate and distinct. 
In dealing with natural phenomena especially, abstraction 
is very seldom fully valid, but may be regarded as justifiable 
so far as it leads to greater knowledge of the objective facts 
studied. 

Summary. — In all its typical forms, abstraction is a method 
of taking, from the context in wilich it is embedded., some 
aspect of a phenomenon in which we are interested. Nega- 
tively, the context is eliminated and stripped off, so far as 
this is possible. Positively, the special aspect studied is given 
a certain unity and self-subsistency by the mind, which not 
only cuts it off from its context, but fixes and names it. 2 
Although the action of our mind is to some extent arbitrary — 
for we select for study any aspect whatever in which ice 
happen to feel interested — we yet aim at objectivity, and 
endeavor to make our abstraction complete. In dealing with 
mind-made entities, this aim can be realised. In- dealing 
with natural phenomena, it can be realised only approxi- 
mately. In all cases, however, the method of taking one 
thing at a time leads, or tends to lead, towards attaining to 
greater insight into the workings of the phenomenon under 
study, and abstraction is thus, as a scientific method, progres- 
sive and fruitful in results. 

2 Hence the danger of hypostatisation. 

FOR FURTHER READING 

B. Bosanquet. Logic, Vol. II, pp. 21-24. B. Erdmann, Logik, (2nd 
Edit.), pp. 65-7S. SS-92. Chr. Sigwart. Logic, Vol. I, pp. 248-259; 
Vol. II. pp. 66-69. W. Wundt, Logik, (3rd Edit.), pp. 11-17. 

EXERCISES 

Show what part is played by abstraction in dealing with the 
following cases: (1) In finding out what has caused a headache. 
(2) In learning a new dance. (3) In translating from a foreign 
language. (4) In correcting papers in a high school subject. (5) 
In selecting a dinner from a menu-card. (6) In choosing a career. 



CHAPTER XXIII 

DETERMINATION 

Nature of Determination. — Determination is the reverse of 
abstraction. Abstraction takes a single element out of its con- 
text and isolates it as strictly as may be, treating it by itself. 
Determination takes an isolated element out of its isolation 
and places it, as far as possible, in a context to which it is 
adapted. In rare cases determination exactly reverses an 
abstraction, and replaces an element in the precise context 
from which abstraction had taken it.. But as a general rule, 
starting with an element which has been thoroughly loosed 
from its original context, we proceed to determine it by plac- 
ing it in a variety of contexts which happen to suit our pur- 
poses, whether the element in question has previously formed 
part of such contexts or not. For instance, starting with a 
single muscle, which abstraction has isolated from its place 
in e. g., the frog, we proceed to determine the nature of mus- 
cular action by placing it upon an electrical machine and 
galvanising it into activity until it is thoroughly fatigued. 
In this case we place it in a context in which it has never 
formed a part, but which throws considerable light upon its 
workings. So too in studying memory. We start with abstract 
entities such as nonsense syllables, and by learning these in 
various types of context of which it is safe to say they never 
naturally formed part, we proceed to determine our memory 
of them in a way which has led to a number of remarkable 
discoveries as to the workings of memory. 

Results of this type are, however, in themselves still some- 
what abstract; and determination proceeds to make them 
more concrete by placing them in contexts which more nearly 
approach the conditions of actual life. Thus, we consider 
how muscular action becomes modified which we have, not 
an isolated muscle functioning by itself, but when we have 
several muscles working together in the organism in a whole. 
Our earlier results with the electrical machine become con- 
siderably modified. We learn, for instance, that in the living 

252 



NATURE OF DETERMINATION 253 

organism no muscle ever becomes completely fatigued, and 
that fatigue seems to be a matter of attention rather than of 
the muscles as such. So too the nonsense-syllable results are 
not, as such, immediately applicable to material which has 
meaning for us, and become determined in a variety of ways 
as we experiment with more concrete contexts. Determina- 
tion is thus a process of rendering ever more concrete the 
results produced by the method of abstraction. 

Negatively, then, determination deprives a given element 
of its splendid isolation, and in so doing usually deprives 
it of part of its clearness and simplicity. But positively, by 
fitting it into a context which is adapted to it, determination 
usually supplies the element in question with accretions of 
meaning, and the new context may make an enormous differ- 
ence to the significance of such an element. For instance, 
a system of ethics constructed in the abstract world of pure 
concepts may be very clear in itself, and very explicit as to 
our duty and our highest good. We must, we are told, aim at 
so acting as to treat others, not as means, but as ends in 
themselves. Another similar precept is to act from pure 
reverence for the moral law, or to aim at loyalty to loyalty 
itself. In the abstract conceptual realm — i. e., in what Kant 
calls the metapJiysic of ethics — these ideas may be extremely 
clear. But when we attempt to apply them in more concrete 
cases, i. e., to determine them in reference to a special con- 
text, they tend to lose much of their abstract clearness, and 
to become mixed up with all kinds of interests, feelings, and 
instinctive desires. Every motive-complex into which they 
enter endows them with new shades of meaning until, in many 
cases, it is almost impossible to discover a trace of the 
original ethical motive. 

So far, we have been considering determination purely 
from the side of the abstract element which we seek to deter- 
mine. But we must also consider it from the side of the con- 
text into which we seek to introduce the element in question. 
This context, in order to admit of the addition of such an 
element, must itself be incomplete and abstract. If the 
element is made more concrete by being placed in the context, 
the context must be made more concrete by the addition of 
the element in question. Determination is two-sided and 
reciprocal. If x is determined in relation to a, 6, c . . , 
a, b, c . . . , are determined in relation to x. Thus, 



254 DETERMINATION 

in the case mentioned above, if the ethical motive is altered 
by its union with the psychological motives, psychological 
motives are often transformed into something higher by 
union with ethical motives — e. #., in the case of love.i In 
fact, such a "context" may itself consist of not more than 
one element, and may be as isolated and abstract as the 
element with which we start. In such cases it is easy to 
see that both become more concrete in their inter-relation, 
and that they determine each other. For example, the con- 
cept of "Becoming" arises, according to Hegel, as a recip- 
rocal determination of the two abstract concepts of "Being" 
and "Not-being." Becoming, that is to say, means the pas- 
sage from one to the other, and is the only way in which such 
abstract concepts can be unified and given concrete meaning. 

One further point remains to be considered. W« have 
spoken so far as though only "elements" were capable of 
being determined. But we saw in the case of analysis that 
it was possible to isolate not only an element but also an 
aspect of a concrete situation. So too with determination. 
We can determine, not only elements, but also aspects. We 
may, for instance, start with a general aspect or view of a 
person's character. This is abstract, for it is divorced from 
knowledge of his ways of acting in specific cases. We may, 
for example, have heard in a general sort of way, that "X is 
a good kind of fellow." If now we are brought into much 
contact with X, it is possible to determine further this gen- 
eral, vague, and abstract outline of his character, and fill it 
out with a wealth of concrete detail. We note his behavior 
in matters regarding himself and his self-interest. We note 
his behavior in matters regarding others, in public as well 
as in private — how he meets his obligations, how he goes 
beyond his strict obligations and likes to do something for 
the other fellow. In each case we acquire a more definite 
and detailed knowledge of his character, or — to express it 
otherwise — the vague indeterminate concept "good kind of 
fellow" becomes thoroughly determinate and clear-cut After 
a year's close association with X, our idea of his character 
has become very definite and specific. 

Determination, then, consists in the synthesis of two or 
more relatively abstract elements or aspects, in the bringing 
these in relation to one another in such a way that, in virtue 
of this relation, each takes on new qualities or characteristics, 

i Cf. Dewey and Tufts, Ethics, pp. 578 ff. 



AIM OF DETERMINATION 255 

and becomes more specific and concrete — as (1) the moral law 
becomes concrete by applying it to a special case of choice, 
and the choice itself becomes ethical by our reference to the 
moral law, or (2) as our insight into X's character becomes 
more concrete by studying his behavior in special circum- 
stances, and our understanding of his behavior in special 
circumstances is made more profound because of our gen- 
eral insight into his character as a whole. 

Aim of Determination (A) Objectivity. — We determine, 
then, by bringing x in relation to a, 6, c . . . and noting 
carefully the resulting modifications. In so proceeding we 
aim, in the first place, at objectivity. It is because we find 
determination an indispensible method in dealing with the 
objective world, that we make use of it. Abstractions may 
be correct, but we tend to find them unsatisfying. They seem 
to belong to the twilight world of mere theory, whereas we 
seek the golden tree of life. How many a student of abstrac- 
tions has felt, like Faust, that he is getting out of touch 
with vital things, and must plunge into the concrete in order 
to recover his mental and moral balance? Mental models are 
of value only so far as they serve to bring us into closer and 
more accurate contact with the objective world. We theorise 
in order to practise, and abstract in order to determine; and 
what we wish to determine is always what we take to be 
what is most real in our experiences. We wish to under- 
stand reality, not only in principle, but also in detail, in 
the concrete. And the first aim of determination is to ensure 
that the concrete detail which our methods bring to light 
shall be objective, and shall bring us into yet closer intimacy 
with nature and ourselves. 

Starting, then, as we do, with elements or aspects which 
are the products of a partially objective analysis and abstrac- 
tion, we hope by comparing these one with another, by turn- 
ing them over and over, inspecting them from all sides and 
in all kinds of relations, to arrive at a still more objective 
understanding of the world in which we live. 

(B) Completeness. — In the second place, we aim at com- 
pleteness, not perhaps in any absolute or final sense, but at 
least at the greatest degree of completeness which can be 
attained. We are never satisfied with acquiring one or two 
new determinations for our concepts. We wish our determ- 
ination to be as complete, as many-sided, and as methodical 



256 DETERMINATION 

as is possible. The complete and final determination of the 
moral law, for instance, or of a person's character, seems out 
of the question for any understanding short of Omniscience. 
But we try to fit the rule to the case as methodically and as 
completely as the nature of the case allows, and by varying 
our viewpoint as much as possible, to take into consideration 
a wide variety of possibilities. 

How Far Realisable? (A) With Mind-Made Entities.— The 
aim, then, of determination is, by bringing x in relation to 
a> b, c . . ., to discover new and concrete modifications of 
x — and also of a, b, c . . . — which are of objective signif- 
icance, and to make our list of such modifications as complete 
as possible. How far can this aim be realised? Let us first 
consider cases from the world of mind-made constructions. 
An engineer who is interested in inventing an air-plane motor, 
for example, has a fair general idea of what conditions are 
to. be met, and of what type of engine is capable of meeting 
such conditions. But his idea is still in part indeterminate. 
He accordingly studies a number of models in actual use, a, 
ft, c . . ., and by comparing closely his ideas with a, per- 
ceives both excellencies and defects in that motor, in such a 
way that his general idea becomes yet further modified, both 
positively and negatively. He next studies b, and obtains 
yet further notions from that study. At the end of his study 
of actual models, the model he has been shaping in his mind 
has become very sharply determined, both negatively and 
positively, and he is now prepared to make and test a new 
model of his own. The determinations which his idea has 
undergone are of some objective significance — for they have 
been made in relation to actual working models, and with 
express reference to the conditions which should be satisfied 
by an ideal model. At the same time, if his comparison in 
the case of each individual model has been exhaustive, it is 
possible for each determination to be reasonably complete, 
and if, further, the number of motor-types in actual existence 
is small, it is possible for the determination as a whole to be 
reasonably complete. Absolute finality in point of objectivity 
and completeness is hardly to be expected, as the history of 
invention shows — for there is always room for yet further 
improvements. But in general, in dealing with machines it is 
possible for determination to assist in producing marked 
improvement over (1) one's own previous ideas or mental 



AIM OF DETERMINATION 257 

models, and (2) the actualised mental models of other inven- 
tors. It is, in short, possible to approach a solution of the 
objective problems rather better than has been accomplished 
by any invention up to date. That is to say, in all such cases 
determination can be both objective and reasonably complete. 

Let us consider another case. We all have a certain vague 
general idea as to the nature of the beautiful. This general 
idea, which is indeterminate and abstract, — i. e., not in close 
contact with the world of actual art-creations — we can make 
more determinate and concrete, by bringing it in relation to 
actual concrete attempts to realise the idea of the beautiful. 
We can study pictures, poems, music, etc. That is to say, we 
can determine our general idea by bringing it into close con- 
tact with actual art-works and asking (1) how our ideal of 
beauty applies to such cases, and (2) how far such works sat- 
isfy our ideal. In this way we gradually educate our artistic 
sense until, from only knowing in more extreme examples 
what we like and what we do not like, we have developed a 
thoroughly concrete and determinate artistic appreciation and 
artistic theory. Such a determinate theory is certainly (1) 
more objective than the general idea with which we started — 
for it has been developed by the closest possible observation of 
artistic models, and has become modified by taking account of 
the various theories which have enjoyed a currency in the his- 
tory of art, so that it is no longer a merely subjective imagin- 
ing which has fed only upon itself — and (2) may be reason- 
ably complete, if we have been careful and exhaustive in our 
study of each separate art-work — though, taken as a whole, it 
can never be fully complete, for the number of actual models 
is very great, while life is short. But a certain well-rounded- 
ness of artistic insight can be attained, just as a certain 
degree of completeness in respect of education in general can 
be attained. On the whole, then, we can state that, in the 
case of mind-made entities, determination can be both objec- 
tive and reasonably complete. That is to say, it can bring us 
into closer and more complete contact with objective conditions 
and objective facts than is possible apart from such determi- 
nation. 

(B) With Natural Phenomena. — In dealing with phenomena 
other than mind-made entities, what is our procedure? In 
the cases from biology and psychology already mentioned, we 
noticed that an abstract theory of muscular action or of the 



258 DETERMINATION 

laws of memory is made determinate by being brought in rela- 
tion to a more specific and concrete context. So too the diag- 
nosing physician tends to have in mind a general hypothesis 
as to the nature of the case which he is examining, and makes 
his general hypothesis more specific and determinate by relat- 
ing it to each symptom in turn. That is to say, he has in 
mind a schematic and indeterminate mental model, which he 
makes more specific and definite by applying it, point by point, 
to the case before him. How far such procedure is objec- 
tive, depends partly upon the objective nature of the preced- 
ing analysis which has divided the case before him into points 
or symptoms. Assuming this to be partially objective, we can 
say that the method of taking a single element of the situa- 
tion and bringing it in relation to the other elements of the 
situation, one at a time — or of taking a mental model of the 
whole and making it more concrete and specific by comparison 
with each element revealed by the analysis — we can say that 
this method is at least as objective as the analysis which has 
preceded it, and that, in practise, it tends to be more objec- 
tive — i. e., to bring those* who use it into closer and more inti- 
mate contact with the objective facts. 

As to completeness, a glance at the progress of science will 
be enough to show us that completeness in any final sense is 
entirely out of the question. For each new generation of 
scientists pushes further, inquiries which were in many cases 
regarded as sufficient by previous generations. In determining 
the concept of arthropod, for example, or protozoon, all that 
can be done is to bring together as carefully as possible all the 
viewpoints and all the knowledge of the period, and thus bring 
the concepts in question up to date. Our textbooks of natural 
science, in fact, represent a kind of cross-section through the 
research and knowledge of the period in which they are writ- 
ten, and all that we can ask of the various determinations 
carried through by writers of a given period is that they 
should be up to date. But the process of scientific inquiry 
does not stand still, and determinations which held good ten 
years ago are now out of date. Some of them have been 
passed by in the race for objectivity, but almost all are now 
regarded as incomplete. Still, as in art and education, so also 
in science. A reasonable degree of completeness can be 
attained. 

Thus we see that in the case of mind-made entities, and also 



VALIDITY OF DETERMINATION 259 

in the case of natural phenomena, progress in objective under- 
standing is always possible, and a certain degree of complete- 
ness can be attained, so that the aim of determination can in 
both cases be approximately realised. In neither case, how- 
ever, can it be completely and finally realised. 

Validity of Determination. — That some determinations are 
fantastic and quite arbitrary, is beyond reasonable doubt. The 
view of the planets as a concrete system of spheres, set in 
motion by "epicycles" or excentrics of a crystalline nature, is 
determinate, and has even some slight objective value. But as 
a serious scientific explanation it has long since been dis- 
credited. The number of epicycles, in particular, which the 
system assumed in order to account for the observed phe- 
nomena, seems to have been quite arbitrary, and for their 
"crystalline" nature the only evidence offered was, that they 
must be of some transparent substance, in order to account 
for their invisibility to human eyes. So too the philosophy of 
nature developed by the speculative philosopher Schelling is 
determinate, but is generally regarded as subjective and arbi- 
trary to the last degree. There is, then, nothing sacrosanct 
about determination as such, and its validity must accordingly 
be a matter of how the method is used. On what conditions 
is determination to be regarded as valid? 

To this question there is only one answer which we can 
give. As a scientific method, determination is valid, if and so 
far as it brings us into touch with objective laws and objec- 
tive facts in a way which leads to an advance in some specific 
science. If it "works" — i. e., if it fits in with the system of 
mental models approved by experience in that particular 
branch of inquiry, and if it also helps to solve our particular 
concrete problem in a satisfactory manner — so far it can be 
regarded as valid. But if it is clear and concrete from the 
viewpoint of intellect alone, or if imagination alone, — as in 
the case of Wolff's Psychologia Empirica or Schelling's Natur- 
philosophie — and fails to bring us into contact with the objec- 
tive world and the realities of experience, it is worthless. How 
far it is valid, then, is a matter which can only be decided by 
the gradual advance of science. There is no easy and simple 
criterion. 

Summary. — Determination, then, is a synthesis of x with a, 
&, c . . . , in such a way that, as thus interrelated, both 
x and a, h, c . . . take on new shades of significance and 



260 DETERMINATION 

become more specific and concrete. The aim of determination 
is to be objective and reasonably complete, that is, to add to 
our insight into objective laws and facts in a way which can 
be accomplished by no other method. In the case of mental 
models and of natural phenomena this aim can, to a reason- 
able extent, be realised. But the extent to which it can be 
realised, and in general the validity of our use of the method, 
is a matter only to be decided in the light of scientific prog- 
ress. So far as determination leads to insight into objective 
structures, and helps us to solve our concrete problems and 
thus advance the science into whose department the problems 
in question fall, its use as a scientific method is justified. 

Abstraction and Determination. — It remains to consider 
briefly the relation of abstraction to determination. Appar- 
ently, abstraction is analytical rather than synthetical, while 
determination is synthetical rather than analytical. Abstrac- 
tion takes an element or aspect out of its concrete context. 
Determination puts an element or aspect into a concrete con- 
text. Abstraction and determination thus appear different in 
starting-point, in result, and in method. But, remembering as 
we do that analysis and synthesis were found to involve each 
other, and to be two sides of a single method, we must ask 
whether abstraction does not similarly involve determination, 
and determination involve abstraction, so that here also, per- 
haps, we are dealing with two sides of a single method. 

Does Abstraction Involve Determination? — Let us begin by 
asking whether abstraction, as such, involves determination 
as an essential part of its method. In abstraction, we take 
an element out of its context. Does our procedure, however, 
render it absolutely contextless? Let us consider. If we 
deprived an element of all context — of all connection with 
and relation to other elements — would it not be cut off from 
the intelligible world and become meaningless? It looks, 
then, as though in taking it out of context a we are perhaps 
putting it into context b; and a little consideration will con- 
vince us that this is precisely what we are, in fact, doing. 
We are always placing it, at least, in a universe of meaning, 
in a system of thought which is intelligible. There is a world 
of concrete realities, and there is a world of abstract mean- 
ings, and abstraction consists largely in taking an element 
out of its place in a particular concrete situation, and giving 
it a different place in the world of meanings. For example, 



ABSTRACTION AND DETERMINATION 261 

the music-student isolates a point of technique for study by 
practising it in a context composed of finger-exercises. He 
ceases to play a certain passage in Liszt or Chopin until he 
has practised that kind of passage in its contexts in the 
finger-studies of Czerny or Hanon. The psychologist isolates 
the "rote" element for special study of memory-factors by 
using the artificial context of nonsense-syllables. That is, 
in fact, how we isolate. We extract the "rote" element by 
using nonsense-syllables. We manage to extract the "double- 
sixths" element by playing the specialised studies in Czerny. 
So too with generalisations. When we generalise, we very 
evidently leave the world of concrete fact and enter the 
world of mental models, the world of scientific hypotheses and 
laws. In this way, then, we see that abstraction involves deter- 
mination, and involves it as an integral part of its method. 
Abstraction from the concrete is at the same time determina- 
tion in terms of mental models, and it is, in fact, by determin- 
ing in terms of mental models that we manage to abstract 
from the concrete. 

Does Determination Involve Abstraction? — Let us now 
reverse our inquiry, and ask whether determination as such 
involves abstraction as an integral portion of its method. If 
we consider the question closely, we see that we are not tak- 
ing an entity which is devoid of context, but rather an entity 
which belongs at least to the world of intelligible meanings, 
in order to give it a context which shall be concrete rather 
than abstract. That is to say, we abstract it, not from a pure 
isolation, but from its meaning-context in order to determine 
it in a more sensory context. As we saw, an element, in 
becoming determinate, tends to lose something. The moral law 
loses much of the clearness and sharpness of outline which 
belongs to it in the metaphysical-ethical world of pure mean- 
ings, and takes on something of the confusion and irregularity 
of our psychological impulses. Our psychological impulses, on 
the other hand, lose much of their merely mechanical nature 
in becoming transformed into something ethical. So too our 
notion of X's character loses its generality and schematic 
nature in becoming specific, and our understanding of X's 
specific acts loses much of its narrowness when envisaged 
from the general standpoint of insight into X's character as a 
whole. It is plain, then, that determination involves abstrac- 
tion as an integral part of its method, and that abstraction 



262 DETERMINATION 

and determination must accordingly be regarded, not as two 
methods, but as two one-sided aspects of a single method. 

Comparison With Analysis and Synthesis. — What is the rela- 
tion of this method to the analytic-synthetic method? In the 
first place, it is a less elementary method. It presupposes 
both analysis and synthesis, and starts, not with a concrete 
situation, but with a context already analysed out into ele- 
ments, or with elements already analysed out of a context. 
In the second place, it takes us further in our investigation of 
objective laws and facts. By taking one thing at a time and 
concentrating our whole powers in a single direction, we are 
able gradually to make further progress than would otherwise 
be possible. As a scientific method whose aim is to place us 
in touch with the objective world, abstraction and determina- 
tion represent a considerable advance upon analysis and syn- 
thesis, a carrying further of the work which the more pre- 
liminary method had begun. 

FOR FURTHER READING 

B. Bosanquet, Logic, Vol. II, pp 168-172. Chr. Sigwart, Logic, Vol. 
I, pp. 265-270. W. Wundt, Logik, (3rd Edit.), Vol. II, pp. 17-19. 

EXERCISES 

Show what part is played by determination in dealing with the 
following cases: (1) In looking up the meaning of a word in the 
dictionary. (2) In selecting courses of study in one's junior year in 
college. (3) In ascertaining the grounds for a gloomy, depressed 
feeling. (4) In choosing pictures for one's room. (5) In choosing 
one's friends. (6) In writing a "report" on an assigned book. 



CHAPTER XXIV 
INDUCTION 

Nature of Induction. — Induction is a highly complex method 
of scientific investigation. It makes use of analysis and syn- 
thesis, abstraction and determination, in all their varieties and 
in any order which suits its problems. What holds together 
this use of these various methods and gives to induction an 
existence in its own right, and specific significance as one of 
the most important of the scientific methods, is its goal. 
Analysis takes apart, abstraction isolates or generalises, but 
induction discovers laws. It is this which distinguishes induc- 
tion from abstraction and determination, which are concerned 
with concepts rather than with laws, though they also estab- 
lish certain empirical generalisations. It is this also which 
marks its importance for science. Analysis and synthesis are 
more preliminary, and deal more with concrete situations. 
Abstraction and determination are more advanced, and carry 
further the work started by analysis and synthesis. But induc- 
tion — and deduction — are the most advanced of all the scien- 
tific methods, and carry to its full completion the work of 
these preliminary methods. The chief aim of investigation is 
the discovery of laws, and induction thus sums up all the other 
methods in itself, and carries their work to its completion, so 
far as this is possible. The nature of induction, then, is to 
discover laws. 

I. — How is this done? There are two main ways, which at 
first sight seem sharply distinct. In the first place, we have 
the kind of generalisation which we have already studied 
under the name of abstraction. In induction this method is 
largely used, but is carried a little further. By taking a 
variety of instances of the problem under investigation, it is 
possible, if we compare them carefully in respect of all the 
points already made clear by analysis, to eliminate a large 
number as immaterial, and thus to narrow the field to such an 
extent that an explanation in terms of some working hypothe- 
sis is more easy to discover. Similarly, by taking both posi- 

263 



264 INDUCTION 

tive and negative instances — that is to say, (1) instances in 
which the particular point in which we are interested is pres- 
ent, and (2) instances closely resembling the former, but dif- 
fering in that the point in question is absent — it is possible, 
by a careful comparison, to eliminate a great deal which is 
immaterial, and thus considerably to simplify our problem. 

For example, if a large number of cases of ptomaine poison- 
ing are reported from a single district, it is possible, by care- 
ful comparison of the chief circumstances revealed by the pre- 
liminary analysis, to eliminate points which vary in the vari- 
ous cases, and to narrow the problem to a consideration of 
the points which remain constant throughout the whole series 
of cases. If A, B, and C were at work on drains, while D, E, 
F . . . were not and yet were poisoned, the drains as a 
possible factor can as a rule be eliminated. Similarly if A, B, 
and C were poisoned, while H, I, J . . . were also at work 
on the drains out were not poisoned — this is a negative 
instance — the drains as a factor to be considered would prob- 
ably be eliminated, at least provisionally. As a rule a prob- 
lem of this kind becomes narrowed down to such a point that 
it is discovered that all were taken ill after their evening 
meal, and that the materials for the evening meal were almost 
all purchased at a single store. It is then possible to carry 
on the same method of elimination of variables until only the 
elements common to every meal are left — such as canned food 
and one or two other items. i When the problem is thus nar- 
rowed down, a hypothesis at once suggests itself, and leads to 
the immediate impounding of samples of the food in question 
for purposes of chemical analysis. 

So too in the famous case of Sir Isaac Newton's experi- 
ments2 to discover the conditions on which the colors of the 
solar spectrum depend. Newton so narrowed the problem 
that he was able to use positive and negative instances which 
were already considerably simplified. A ray of sunlight 
entered the dark room of his physical laboratory, and shone 
upon a screen, making a whitish or yellowish circle of light. 
The spectral colors not being present, this furnished a nega- 
tive instance. By inserting a glass prism into the path of 

i Such cases are only too common. In the particular case which 
came under the writer's notice — in Berlin in 1913 — the causa mail was 
German sausage. 

2 A careful discussion of the inductive methods involved will be 
found in S. H. Mellone's Logic. 



NATURE OF INDUCTION 265 

the ray, Newton was able to produce the colors upon the 
screen. This furnished a positive instance. The production 
of spectral colors from the ray of sunlight was thus due to 
something in the nature of the glass prism. Analysis showed 
that prisms might vary in size, in shape, and in material. 
Abstraction suggested devising special experiments to test 
each one of these special possibilities, both positively and neg- 
atively. In these experiments, size was totally eliminated, 
material was partly eliminated, and certain kinds of shape 
were eliminated, other kinds being thus made more deter- 
minate. The problem being thus narrowed down, the hypothe- 
sis of the composite character of sunlight suggested itself, 
and was subsequently verified. 

II. — In the second place, we have a method which seems 
more akin to determination. We frame a possible explana- 
tion of the case before us, and then proceed to modify or deter- 
mine this hypothesis by bringing it into connection with the 
points revealed by analysis, one by one. What is superfluous 
or erroneous in the hypothesis or mental model becomes elimi- 
nated and corrected, until finally it fits the facts as closely as 
we can make it. For example, in the work of criminal inves- 
tigation, a detective constructs a hypothesis to account for the 
facts, and proceeds to determine it further by following up 
specific clues, until a satisfactory conclusion is reached. So 
too in prospecting for minerals, it is usual to start with a 
general hypothesis based partly on general mineralogical infor- 
mation, partly on special local knowledge, and to determine 
this hypothesis by testing for ore here and there until a com- 
pletely satisfactory conclusion is reached. More particularly, 
the method consists in framing a hypothesis, and then deduc- 
ing from the nature of the hypothesis or mental model certain 
specific consequences, which can be brought into more imme- 
diate relation to the facts of the case. If these do not fit the 
facts, the hypothesis is modified until the deduced conse- 
quences and the observed facts more nearly coincide. This is 
brought out with especial clearness in Huxley's marshalling 
of the evidence for the evolution hypothesis. He first deduced 
what, assuming the hypothesis to be correct, one would expect 
the facts to be in a specific case — the case being concerning 
certain anatomical details to be expected in the ancestors of 
the horse — and then showed that the actual examples dis- 
covered and placed in the Yale museum agreed with the deduc- 



266 INDUCTION 

tions in question. He even proceeded to make further prophe- 
cies in the shape of deductions along the same general lines, 
and these deductions have been verified by more recent dis- 
coveries.3 

This second method of induction, which proceeds by framing 
mental models and then determining these, does not seriously 
differ, when we come to look closely at both, from the method 
of generalising by means of abstraction. In the first place, 
they look like two phases or halves of one and the same 
method. Thus, when the problem of poisoning had been sim- 
plified to a certain extent, the subsequent procedure consisted 
in framing a hypothesis about the canned food, and then deter- 
mining this further by means of chemical analysis. So too in 
the case of Newton's experiment — the hypothesis of the com- 
posite nature of sunlight was suggested after the problem had 
been partially simplified, and was subsequently further deter- 
mined. That is to say, it looks as though the method of induc- 
tion consisted of approximately three phases:' — (1) analysis 
and simplification of the problem, (2) construction of some 
hypothesis on the basis of the simplifying analysis, and (3) 
determination of the mental model thus suggested, by careful 
comparison with the facts. This last stage is sometimes 
known as Verification. 

But, in the second place, it is possible to look into the pro- 
cedure still more closely, and to realise that it is less with 
two successive phases, and more with two simultaneous 
aspects, of the inductive method, that we have to do. The 
method of abstraction and generalisation, which results in 
eliminating certain factors, really proceeds itself by the help 
of mental models, and thus may reasonably be regarded as 
itself a determination of some general hypothesis, or making 
it more specific. In the poison case, the general hypothesis 
concerns the source of the poison, and this hypothesis cer- 
tainly is present in the beginning and becomes determined 
and narrowed down with each step in the inquiry. In fact, 
the whole problem may reasonably be regarded as an attempt 
to determine the source of the poison. So too Newton had a 
general idea that there must be something in the nature of 
sunlight which made it possible for the spectral colors to be 

3 See Huxley's lecture, The Demonstrative Evidence of Evolution. 
It is quoted, with a few omissions, by A. L. Jones, Logic, inductive 
and deductive, pp. 287-300. 



AIM OF INDUCTION 267 

produced in his experimental laboratory, and each step in the 
experiment may legitimately be regarded as making this gen- 
eral idea or hypothesis more determinate and specific. So too, 
on the other hand, by following up special clues, the detective 
is learning what may be eliminated, and by his special tests 
the prospector is discovering what sites may be regarded as 
unpromising and negligible. There is thus one complex 
method, which results in the discovery of some principle or 
law. 

Aim of Induction (A) Objectivity. — Induction, then* is a 
highly complex method, which employs all the resources of 
analysis and synthesis, of abstraction and determination, until 
our mental models approximately fit the facts under consid- 
eration, and we are thus able to discover some principle or 
law. The aim of induction is, first and foremost, to be objec- 
tive. We do not wish to discover some hypothesis which sat- 
isfies us, but turns out to be fatastic or unverifiable, when 
brought into connection with the actual facts. We seek to 
discover objective laws, laws which really seem to apply to 
the facts. Sometimes it is in terms of causal models, some- 
times in terms of mathematical models, sometimes in terms 
of models which belong to a more specific branch of scientific 
inquiry, as when we seek to discover the principle which holds 
a particular botanical theory together, or which unifies the 
various ways in which a particular term is used in literature. 
The use of the various scientific methods in order to discover 
a principle or law which is of objective significance, is the 
primary aim of induction, whether the principle is causal, 
mathematical, or what not. 

(B) Completeness. — In the second place, induction aims at 
completeness. As we saw, the characteristic which distin 
guishes induction from the methods previously considered, is 
that it carries their investigation further. That is to say, it 
aims, not only at a greater degree of objectivity, but also at a 
greater completeness of investigation. Abstraction is satisfied 
with isolating some special element or aspect. Determination 
is satisfied with making some such element or aspect concrete 
and specific. Induction aims at carrying the investigation 
further, and abstracting or determining the law which governs 
the case in question — and at discovering it as completely as 
may be possible. It is usually thought that induction is never 
perfectly complete, and that science aims at progressiveness 



268 INDUCTION 

and fruitfulness in its solutions, rather than at formulations 
which are to be accepted as final. But there can be no doubt 
that it is satisfied with nothing less than the fullest determi- 
nation of which the evidence admits. Objectivity, then, and 
completeness represent our aim in using the method of induc- 
tion. 

How Far Realisable? (A) With Mind-Made Entities.— Give 
a college graduate one of the psychological puzzle-boxes, and 
ask him to find out the principle in accordance with which it 
can be opened and shut. For convenience of reference, let us 
consider the box to which we previously referred.* A little 
experimenting completes the work of analysis and synthesis. 
The factors are learnt to be (1) the two levers, (2) the bolt 
which falls by its own weight when both levers are drawn out 
and the box is placed upon the white side, and (3) the com- 
bination lock. Abstraction and determination further are 
brought to bear upon (1) and (2), until the principle which 
governs them is discovered. Then the combination lock is 
experimented with, in terms of one mental model after 
another, until the limits within which it works are finally 
determined. These items of knowledge thus ascertained, their 
application, in the proper order, to the different elements of 
which the works of the box are composed, will open the door. 
The student is now possessed of the principle. His induction 
is certainly objective, for it works. He can actually open the 
box before him. He understands the principle of the thing. 
His insight can reasonably be regarded as complete. For what 
remains to be discovered? Once the box is opened, the struc- 
ture, at which he had previously guessed, becomes visible, and 
even the combination lock can be taken to pieces without much 
difficulty. It is true that certain ultimate problems in physical 
science — e. g., as to the nature of levers, including the ques- 
tion why one end should move when we move the others — 
remain unsolved. But those go beyond his problem. His 
problem was to open the box, and to find out the principle of 
its works. He has opened the box, and has found out the 
principle. His problem is solved, and his induction can thus 
be regarded as not only objective, but also complete. 

Let us consider another example. In working out a text- 



4 Of. p. 221 above. 

5 Cf. Sir Oliver Lodge, The Survival of Man, p. 81. 



AIM OF INDUCTION 269 

book problem in simultaneous quadratics, the first thing to do 
is to get the conditions stated in terms of #2 and y%. This 
represents the work done by analysis and synthesis, and in 
the case of most text-book examples is practically done for us. 
Then follows the work of abstraction and elimination, and 
this complex procedure is continued until eventually we have 
eliminated everything on one side of our equation but x, and 
on the other side everything but a numerical value — say 5. 
We then go back to our first mental model, e. g., an equation 
of the form 2x% — J f xy-\-y^=50 and, by substituting for x its 
numerical value 5, are able to eliminate x and thus determine 
y, eventually discovering that y=20. In this way we have 
discovered the principle or law which we were seeking. The 
result is objective, for it is obtained by rigorous operations 
upon the analytic-synthetic reconstruction of the data. It is 
also complete, for the problem is solved. It is true that the 
solution of equations presupposes answers to a number of 
mathematical, logical, and even metaphysical questionings, but 
these lead beyond the problem with which we were dealing. 
That has been definitely solved. If such cases are to be con- 
sidered as typical, we can say that in the case of mind-made 
entities, where thought is dealing with itself and its own con- 
structions, our inductions can be both objective and complete. 
(B) With Natural Phenomena. — In cases where thought has 
to deal with phenomena other than its own constructions, the 
path to objectivity and completeness does not seem so certain. 
We proceed, by constructing mental models, and by a process 
of trial and error which eliminates the less promising of these, 
to simplify our problem in various ways, using analysis and 
synthesis, abstraction and determination, until in the end we 
have brought our mental model as close to the objective laws 
and facts as seems in our power, and have made it as com- 
plete as we can. There is, however, as we have seen before, 
always some gap between our mental models and the empirical 
facts. For instance, in using the mathematical type of model, 
we might even use one in the form of simultaneous quadratic 
equations — thus to some extent resembling the mind-made case 
mentioned above. Once our data are expressed in algebraical 
form, a conclusion can be worked out which is both objective 
and complete so far as the mathematical conditions are con- 
cerned. But between a given school-book example and a real 
problem in physical science, there is all the difference in the 



270 INDUCTION 

world. The school-book example is mind-made, and can be 
fitted completely and without remainder into the equational 
form in question. But the phenomena dealt with in physical 
science are seldom, if ever, of this exact form. There is in 
practise always a certain marginal error, and our examples, 
as a rule, refuse to work out nicely. We cannot quite over- 
come the gap which separates our models from the phenomena 
which we are studying, though we can, by improved methods 
of determination, reduce this gap to very small proportions. 
In the case of the poisoned workmen, for instance, the methods 
employed rarely prove in a way which could be regarded as 
completely satisfactory that the poison came from the canned 
food. "We need the further chemical analysis, and till that has 
been performed, we tend to suspend judgment. Even the 
chemical analysis is not perfectly satisfactory. So too in crim- 
inal cases, circumstantial evidence may point strongly in one 
direction, and may still be entirely misleading. In fact, in 
dealing with such phenomena, our methods seem to be like 
those of indirect proof; where direct insight is not to be had. 
Inductive methods, in such cases, seem like an attempt to sub- 
stitute painstaking completeness for direct insight. We try, 
by proceeding both positively and negatively, so to manipu- 
late the analysed data, .that one mental model seems highly 
probable and all alternative explanations which could reason- 
ably be framed are shown to be improbable, and are thus 
eliminated. But nothing short of direct insight is perfectly 
satisfactory, and in dealing with natural phenomena we have 
put up with something short of direct insight, and can thus 
only approximate to realising the aim of objectivity and com- 
pleteness. 

Types of Inductive Method. — The chief types of inductive 
method are the mathematical and the causal. That is to say, 
we can distinguish inductive types in terms of the type of 
mental model employed. In practise, however, these repre- 
sent only the two chief forms. Strictly speaking, there are at 
least as many types of inductive method as there are specif- 
ically distinct sciences, and as these are not only indefinite, 
but also increasing in number, it seems unprofitable to attempt 
in any way to sum them up. Attempts have been made to dis- 
tinguish inductive methods according as positive instances 
alone are employed, or a mixture of positive and negative 
instances, etc., but in practise all instances are partly positive 



VALIDITY OF INDUCTION 271 

and partly negative,^ so that it is unwise to attempt to intro- 
duce distinctions which are without practical — i. e., objective 
— significance. The only safe statement for us to make is, 
that induction is a highly complex method of scientific inves- 
tigation, which feels its way by means of analysis and syn- 
thesis, abstraction and determination, until it reaches some 
approximation to insight into the law for which it is seeking. 

Validity of Induction. — In dealing with mental structures — 
i. e., with cases in which it is possible to attain to an insight 
which is both objective and complete — it is easy to test the 
validity of an induction. An induction is valid which really 
leads to such insight. When we have reached the principle 
which makes clear the fastening of our puzzle-box, or the solu- 
tion of the problem in simultaneous quadratics, we know that 
our induction has been valid, because it works in a way which 
we can test directly, and can understand. But in dealing with 
natural phenomena, where such direct insight is out of our 
power, our inductions can only approximate to full validity. 
In such cases, we can say that they are valid so far as they 
work — i. e. y so far as they enable us to understand the law in 
question. For example, if we can predict, from our approxi- 
mate insight into some such law, what will happen in a given 
case, and experience really fulfills our prediction, — if we can 
handle phenomena much as though they were mental models — 
as we seem able to do in calculating eclipses — so far we can 
regard our inductions as valid. But for approximation to a 
progressively more objective and more complete insight into 
the structure of natural law, we must look to indefinitely con- 
tinued inductive inquiries — i. e., to the development of empir- 
ical science itself. It is only in the light of wider and deeper 
knowledge that we can judge whether our present experiments 
are leading in the right direction or not. The "right" direc- 
tion is the one which leads to a more objective and more com- 
plete knowledge of the laws which seem to underlie natural 
phenomena. 

Summary. — Induction is a complex method of investigation 
which sums up in itself the work of analysis and synthesis, 
abstraction and determination, and carries this work further, 
until it discovers some law. Its aim is objectivity and com- 

6 For example, the "positive" instances agree in the presence of 
the phenomenon in question but disagree by varying in many other 
respects. That is to say, in respect of points other than the phenom- 
enon in question, such instances are "negative." 



272 INDUCTION 

pleteness, and this aim can be realised with mental structures, 
but not precisely with natural phenomena. The validity of 
induction is tested by inquiring how it "works," and can thus 
be settled only by more prolonged experimentation, i. e. t by the 
progress of science itself. 

FOR FURTHER READING 

B. Bosanquet, Logic, Vol. II, pp. 175-179. F. H. Bradley, Principles 
of Logic, pp. 329-342. B. E r dm a nn, Logik, (2nd Edit.), pp. 742-754, 
774-784. H. W. B. Joseph, Introduction to Logic, chapters xviii-xix. 
Chr. Sigwart, Logic, Vol. II, pp. 288-311. W. Wundt, Logik (3rd 
Edit.), Vol. II, pp. 20-30. 

EXERCISES 

How might the following cases be investigated inductively : ( 1 ) 
The theft of a sum of money from a room in a hospital to which 
only three nurses have access. (2) The comparative teaching efficiency 
of three grade school teachers. (3) The meaning of "Imagination" 
in Aristotelian psychology. (4) The comparative efficiency of party 
government and non-partisan government. (5) The degree of accuracy 
with which we can localise touches on the forearm. (6) The effect 
of wave-action upon rock. (7) The rate of growth of the different 
bodily organs. (8) The chemical constitution of a given substance. 

(9) The significance of the Biblical version of Nebuchadnezar's defeat. 

(10) The value of memory-training in increasing intellectual ability? 



CHAPTER XXV 
DEDUCTION 

Nature of Deduction. — Deduction is the reverse of induc- 
tion. Induction reasons from specific instances to a law or 
general principle exemplified in those instances. Deduction 
starts from a law or general principle, and reasons from the 
principle to its consequences, or from the law to its workings 
in some special case. Deduction is in every respect fully as 
complex as induction, and may make use of experimental 
abstraction and determination, as well as of the more general 
and simple methods of analysis and synthesis. Thus, starting 
with the general principle that life insurance is a good thing 
and that we ought to insure our lives with the best possible 
company, it takes a great deal of analysis and synthesis, 
abstraction and determination, before we can be certain which 
is the best possible company, and can thus apply our principle 
to a definite instance. Or we may start with an ethical prin- 
ciple such as "All rational beings as such are to be treated as 
ends-in-themselves, and not as mere means to our ends," and 
deduce from it as a consequence the specific principle that 
children and imbeciles, criminals and animals, not being fully 
rational, cannot be treated in this way, but must have their 
"ends" set for them by the more rational elements of society. 
It has even been argued by men of high education, such as 
Aristotle and even Plato, not to mention more modern 
instances, such as Nietzsche, that people of relatively low 
education, and all animals, are definitely to be exploited, and 
find their highest development in serving the higher ends of 
more rational people. Just how far this principle is to be 
applied in practise, is doubtful. But in any case, the deduc- 
tion of specific consequences requires special experience, and 
a considerable amount of abstraction and determination. 

One of the aspects of deduction which makes it of special 
value as a method of scientific investigation, is that it does 
not require a law to be already established in order to have a 
starting-point, but can assume a hypothesis provisionally, and 

273 



274 DEDUCTION 

then ask, Given such and such a law, what would follow from 
it? This experimenting with mental models is of the greatest 
value when we are dealing with complex situations into which 
we have little direct insight. For example, the Copernican 
hypothesis was first worked out in this provisional and experi- 
mental way, until the coincidence of its deduced consequences 
with the observed facts made it universally accepted. So also 
in dealing with complex geometrical problems, we tend to 
assume various hypotheses and ask what follows from them, 
until we hit upon one which seems acceptable. The same 
procedure is adopted in dealing with causal models also. It is 
even possible, in cases where our actual knowledge is extremely 
slight, for us to assume successively (1) a certain provi- 
sional hypothesis, and (2) its opposite, and then deduce con- 
sequences from each of these hypotheses until, by means of 
these consequences, we succeed in bringing our assumptions 
into contact with actual or possible experience. We can then 
decide directly between the groups of consequences, and thus 
indirectly between the opposed hypotheses. This we do fre- 
quently when it is a question which of two alternative plans 
we should follow in some complex problem of conduct, but 
the "method of hypotheses," as it is called, has been employed 
in philosophy since the time of Zeno and Plato, and under the 
name of "multiple working hypotheses" is employed, in a 
slightly more complex form, in modern science. 

Perhaps the most noticeable characteristic of deduction is 
its logical consistency. By means of deduction we build up 
mental patterns which are all of a piece. We cannot deny a 
single consequence without denying the principle with which 
we started, and without at the same time invalidating all 
other consequences which have been deduced from the same 
principle. If we can deny that two plus two make four, we 
are at the same time denying, not only the truth of all the 
principles upon which arithmetic rests, but also the whole 
body of the science, so far as it depends upon these principles. 
We are denying, for instance, that 2+4=6, that 20 — 10=10, 
etc. On the other hand, each consequence which proves accept- 
able, strengthens the main principle, and also an argument in 
favor of accepting other consequences. If this medicine was 
good for John, when he had the measles, and for Mary in 
similar circumstances, and for a number of other people whom 
we know, then it will be good for us too. There must be some 



AIM OF DEDUCTION 275 

principle underlying the previous cases, and it is reasonable 
to assume that our case also will come under that principle. 
This mode of thinking is especially important in the science 
of healing, but applies also to almost all of the more developed 
sciences. Where observations have been correlated for a great 
number of years, a body of science gradually grows up which 
constitutes a system, and is all of a piece, in such a way that 
we can confidently apply its principles even beyond the hith- 
erto observed types of case. 

As a method of scientific investigation, deduction is used 
chiefly in drawing consequences from the mental models which 
we have constructed, whether these models are merely provi- 
sional, or have been made in accordance with principles 
securely established upon a basis of constant experience. 
These consequences may then be compared with the observed 
facts or with the known laws in the special science of which 
they form a part. In special cases, they may even be com- 
pared with the general principles of consistency. If the con- 
sequences do not agree with the known facts, we know that 
the model we have assumed for the purposes of understanding 
a concrete situation, does not apply to that situation. If they 
do not agree with what are regarded as known laws in their 
special field, we must conclude that there is something wrong, 
either with our model, or with the ''known laws" — if not with 
both. If, finally, the consequences of a principle lead to notice- 
able inconsistencies among themselves, that is evidence that 
the model itself contains logical flaws, and has been wrongly 
constructed.! The nature of deduction, then, consists in rea- 
soning consistently from principles to consequences, and in 
scientific investigation more particularly consists in inferring 
to the consequences involved in the mental models which we 
employ for our various scientific purposes. 

Aim cf Deduction (A) Objectivity. — The consistency which 
is the chief characteristic of deduction is not an end in itself. 
For purposes of scientific investigation our aim in deducing 
consequences is to get into touch with objective facts and 
laws. Spinning thought-webs is, in itself, valueless to the 
scientist. He is interested primarily in discovering laws and 
testing the objective validity of hypotheses in his special field, 
and thus the first and chief aim of scientific deduction is 
objectivity. Deduction is valuable as a scientific method of 
investigation precisely so far as it brings us into closer touch 

i Cf. Plato, Parmenides, esp. 12TE-128D. 



276 DEDUCTION 

with the objective world than would be possible without its 
aid. Without it, we might, perhaps, be able to construct 
brilliant hypotheses, but we should certainly remain unable 
to verify them in any way, or even to choose wisely between 
rival explanations of the same phenomenon, because we should 
not be able to connect them up with our empirical observa- 
tions. A great portion of the usefulness of deduction to 
science, consists in its being the main highway along which 
we can pass from our mental models to the actual facts, and 
thus verify hypotheses and establish laws. Objectivity, then, 
is the first and greatest aim of deduction. 

(B) Completeness. — In the second place, deduction aims at 
completeness, or at least at reasonable completeness, a com- 
pleteness such as sufficiently meets our problem and safe- 
guards our conclusions. We do not, as a rule, attempt to 
deduce all the possible consequences of a principle, but only 
the more striking types of consequence, and more especially 
such consequences as can be brought in definite relation to 
the concrete situation, and can furnish "test cases" for the 
mental model which we are applying. In order, however, to 
realise the aim of objectivity, it is necessary for us to avoid 
superficiality and one-sidedness, and thus to deduce a con- 
siderable variety of consequences. By "reasonable complete- 
ness," then, is understood that deduction aims at drawing a 
variety of consequences, which on the one hand are appro- 
priate to the concrete situation, and on the other are sufficient 
in number to strengthen our conviction of the objectivity of 
our procedure. 

How Far Realisable? (A) With Mind-Made Entities. — 
How far can this aim be realised? How far is it possible 
for us to deduce consequences from principles in a way which 
shall be both objective and reasonably complete? Let us con- 
sider an example. If we understand the principle which 
governs the working of our psychological puzzle-box, we can 
deduce just what will take place if, e. g., we pull the two 
levers in the wrong order, or if we turn the box on its white 
side before pulling the levers, and then turn it back again 
before pulling the second lever; or if we turn the combina- 
tion lock twice to the right, as indicated, but only once to 
the left, or if we stop at the wrong figure, etc. So too if we 
understand the principles of harmony and the structure of 
the piano, we can apply our knowledge in such a way as 



AIM OF DEDUCTION 277 

to enumerate the chief concords and discords, and explain just 
what physical phenomena — e. g., in the way of "beats" — will 
take place when such and such notes are struck together. 
In such cases our deductions are certainly objective. For the 
object to which we refer is nothing but a concrete embodi- 
ment of the precise principles whose implications we are 
making explicit, and every one of the consequences drawn 
can be verified by reference to the facts. In dealing, then, with 
objects of this kind, where the object is constructed in terms 
of a plan which is rational, it is possible to deduce the con- 
sequences implied in the principle of the plan, and such 
consequences will be found to hold good of the object itself. 

What are we to say of completeness? If such deduction is 
objectively correct, if, e. g., we deduce precisely what happens 
when we turn the combination lock only once to the left, it 
could not well be more complete — at least for practical pur- 
poses. It is true that a physicist's understanding of the 
nature of the material employed and the various physical 
laws involved would theoretically be more complete, though 
even in physics any final completeness is out of the question. 
But the problem is not properly concerned with the physical 
nature of the material, but with the material only so far as 
it is the embodiment of a rational plan. Our deduction has 
solved its special problem completely. But if we regard deduc- 
tion as reasoning, not to a single consequence of the principle, 
but rather to a reasonably complete variety of consequences, 
so that the truth of each will reflect credence upon the others 
and will also strengthen our confidence in the principle — we 
see that an absolute completeness is out of the question. The 
success of each of our inferences strengthens the conviction 
that we have really grasped the plan according to which the 
box has been put together, and our aim is not to deduce every 
last consequence, but only a sufficient variety and number to 
avoid one-sidedness and provide an adequate test of the prin- 
ciple. This, however, can be done, in the case of the box, 
and in the case of the piano, and it seems fair to state that, 
so far as mind-made apparatus is concerned, our aim can be 
realised, not only in respect of objectivity, but also in respect 
of completeness. 

Let us examine another example. When once we have 
grasped the principle of the bi-litteral cipher, and realise 
that a group of five letters is to represent a single letter of 



278 DEDUCTION 

the alphabet, and that in selecting the members of each group 
we are restricted to some combination of the two symbols 
A and B — we can deduce at least as many consequences as 
there are letters of the alphabet. Thus, we can deduce that 
AAAAB = a, AAABA == &, AABAA = c, ABAAA = d. . . . , 
etc. In fact, the reading of the cipher message is itself a 
complex consequence of the principle, and the most convincing 
consequence too. The drawing of consequences is in such 
cases a kind of construction — for by this means we construct 
the details of the mental model in question — and if this con- 
struction agrees in its details with the details of the given 
problem AAA BB. . . ., the problem is solved. Such deduc- 
tion is certainly objective — for it enables us to read the 
cipher message — and reasonably complete — for it enables us 
to construct a whole alphabet, and indeed, any number of 
cipher messages which could be understood by the transmitter 
of the original problem. If such examples are to be regarded 
as typical, we may state that in dealing with mental models, 
the aim of deduction can be realised. 

(B) With Natural Phenomena. — We deal with natural 
phenomena, as we have seen, primarily through the medium 
of mental models. We construct a model in terms of some 
rational plan, and then deduce its detailed consequences with 
a view to comparing these with the details of the phenomenon 
in question. If the mental model fits the phenomenon in 
detail, we regard the principle of both as practically identical,! 
and are satisfied that we have practically discovered the law 
of the phenomenon in question. So far as deduction is con- 
fined to elaborating the consequences of our mental model, 
so far the account given under the head of "mind-made 
entities" holds. good. But in dealing with natural phenomena, 
we mean something more. Does our deduction in any sense 
take us beyond the realm of mind-made models, and bring 
us into contact with the objective world? Is deduction objec- 
tive in this sense? Let us consider an example. In trying 
to understand the principle of the basilar membrane, some 
scientists use the model of the wires in a grand piano, while 
another group use the model of the membrane in a telephone. 
In both cases, consequences are deduced from the nature of 
these models and compared with the experimental evidence. 

i Cf. William James, Pragmatism, lecture I. 



TYPES OF DEDUCTION 279 

Has this kind of deduction a significance which is objective? 
Yes, it certainly does help to bring us into closer and more 
intimate contact with the meaning of the phenomena in 
question. It is not at the present day possible to state that 
either of these models is perfectly correct, but the deduction 
of consequences from both models, and the experimental 
attempts to verify the theoretical deductions in terms of 
the actual facts, have undoubtedly led to a great increase 
in our knowledge of the objective conditions and facts of the 
case. So far, then, as objectivity is concerned, the aim of 
deduction can be at least partially realised in this field. 

In respect of completeness also something can be done. The 
deductions as such are from the principle of the mental model 
to the details of the mental model, and so far as our thought 
is confined to the realm of mental models, each such deduc- 
tion can be regarded as complete. But when we transfer the 
question to the world of natural objects, this is no longer the 
case. There is, as we have already seen, always a certain 
gap which separates our models from the concrete realities. 
The reality is always something more detailed, for instance, 
than we seem quite able to grasp. Nature, as we say, has an 
infinite variety. This gap, this difference between what we 
seem able to construct on the one hand, and the objective 
phenomena on the other, is a measure of the extent by which 
we fall short of completeness. We cannot deduce all the 
details of the phenomenon because we have not perfect insight 
into the law in question. Certain of the more important and 
striking consequences we can deduce, where our knowledge 
is well developed. But completeness is more than we can 
expect. In dealing, then, with natural phenomena, the aim 
of deduction, in point of objectivity and completeness, can 
only partially be realised. This partial realisation, however, 
is certainly valuable, not only in itself, but also as leading 
to further progress in scientific discovery. 

Types of Deduction. — There are two main types of deduc- 
tion, the mathematical and the causal. That is to say, we 
can distinguish deductions in terms of the type of mental 
model whose consequences are deduced, and — as we have 
already seen — the most commonly found, and most generally 
valuable types of mental models are precisely those which 
belong to the mathematical and causal groups. But mental 
models are by no means confined to these two types. On 



280 DEDUCTION 

the contrary, there are at least as many possible types as 
there are specifically distinct scientific viewpoints. But these 
are indefinite in number, and are also tending to increase as 
science takes in more fields of inquiry, and it is thus not, per- 
haps, possible to confine within any rigid limits the number 
and types of mental models. In consequence, we cannot 
restrict in any way the number of typical forms which can 
be used in valid deduction. The types of deduction are innu- 
merable. In the history of logic, attempts have, indeed, been 
made to work out all the forms of valid deduction which the 
mind could possibly use, but as the most notable attempt 
restricted thought to following the detailed developments of 
a single mental model, and that too neither quantitative nor 
causal — we must regard it as bold but unprofitable. Thought 
cannot be restricted to the use of any single group of models, 
but is as various and complex as it finds advisable in dealing 
with the problems which arise. As it is clearly impossible to 
limit such problems, so it is impossible to limit the forms of 
deduction which can be used in solving those problems. 
Thought is free and unfettered. All we can safely say is 
that, at the present stage of science, the mathematical and 
causal types are the most frequent and the most universally 
valuable. 

Validity of Deduction. — That deduction is not always objec- 
tively valid will be plain if we consider briefly a few typical 
cases. Hemlock Jones in the story deduces with convincing 
clearness that Potson has stolen his pipe — and the pipe is, in 
fact, in Potson's pocket. Potson realises that it would be 
quite impossible to convince Jones that his ingenious deduc- 
tion is invalid, though he knows it to be wrong. So too the 
paranoiac deduces with almost flawless completeness that all 
the world is in a conspiracy against him — and indeed they do 
actually put him under restraint in the end. It would be quite 
impossible to persuade him that his deductions are unsound, 
and yet we know that they are. It is possible, in short, to 
explain one and the same fact in terms of a variety of mental 
models, and yet certain of those mental models may be radi- 
cally mistaken, as when Bain tries to explain parental affec- 
tion in terms of the benefits to be returned in after-years, or 



2 The reference is to the Aristotelian syllogism. Aristotle himself 
believed this to be a causal model, the "middle term" being identical 
with the cause. But this is today generally regarded as a mistake. 



VALIDITY OF DEDUCTION 281 

Mill tries to explain universal benevolence in terms of ego- 
istic self-seeking. There are thus cases of deduction which 
seem convincing enough from the viewpoint of consistency- 
alone, but are found to be inadequate when we apply them 
to the actual world. What, then, is the criterion? How are 
we to distinguish a valid from an invalid deduction? To this 
question we can only answer that there is no simple criterion. 
In order to test our deductions and discover whether they are 
objectively valid or not, our only final criterion is the progress 
of science itself. If the mental model which we have used is 
found to be helpful in the concrete situation, and also fruitful 
in suggesting and solving further problems — if, in short, it 
"works" — we may regard it as so far valid. If, however, like 
Bain's insurance model applied to the case of family affec- 
tion, it seems to solve the case before us, but brings us into 
hopeless conflict with the models of explanation accepted as 
verified in all kindred researches, and is of no avail to solve 
further problems — there is so far reason to regard it as invalid. 
In the case of natural science, then, the only adequate test 
of the objective validity of deduction is the further progress 
of the science itself. In the case of mind-made entities, how- 
ever, we have already seen that deduction can be objective. 
In such cases it is a mere matter of consistency, and of that 
we are fairly good judges, especially in the simpler instances. 
In complex cases, analysis is necessary, and only the 
advanced thinker can come to valid decisions. 

Summary. — Deduction, then, is a process which makes 
explicit the consequences implied by some principle or law, 
whether such law is already established, or is merely assumed 
as a provisional hypothesis. Its chief aim is to bring us into 
closer touch with the objective facts than would be possible 
without its aid, and to be not only objective, but also reason- 
ably complete. This aim we can accomplish in dealing with 
mental models, but can only approximate to attaining in the 
case of natural phenomena. In such cases the validity of our 
deductions can be appreciated only as science itself advances 
by such means. In general, however, it may be confidently 
asserted that deduction is a valuable factor in securing such 
an advance. 

FOR FURTHER READING 

Chr. Sigwart, Logic, Vol. II, pp. 181-192. W. Wundt, Logik, (3rd 
Edit.), Vol. II, pp. 30-38. 



282 DEDUCTION 

EXERCISES 

How might -the following cases be investigated deductively: (1) 
The comparative efficiency of learning a long poem as a whole, or 
as a number of sections. (2) The value of the ergograph as a test 
of mental fatigue. (3) Whether black is or is not a positive sensa- 
tion. (4) The best method of holding the hand in writing. (5) The 
most efficient method of practising at the piano or violin. (6) The 
scientific value of psychological or pedagogical study. (7) The best 
time for planting corn. (8) The means by which the automatic chess- 
player (described by E. A. Poe) was worked. (9) The practical 
value of a college education. (10) One of the Sherlock Holmes 
problems ? 



CHAPTER XXVI 
INDUCTION AND DEDUCTION 

The Problem. — Owing to historical associations, induction 
and deduction have become watchwords of scientific and 
logical thought. Many of our elementary manuals to this day 
are entitled "Logic, Deductive and Inductive," as though 
deduction and induction together exhausted the field of logical 
inquiry. There are even well-known books published on 
Deductive Logic alone, and on Inductive Logic alone, and 
many writers who treat of both, do so in separate volumes. 
We have, then, a tendency, owing to historical considera- 
tions,! to regard induction and deduction as separate, and 
even opposed, methods. Deduction, in our minds, stands for 
Aristotle and mediaeval thought with its emphasis on argu- 
mentation and clear ideas, and its almost total lack of experi- 
mentation and discovery. Induction similarly stands for mod- 
ern science, with all its empiricism and distaste for arm-chair 
methods, and with its extreme insistence upon observation 
and experiment. We even tend to think of deduction as the 
method of mere proof, of organisation of knowledge obtained 
from some non-deductive source, while induction seems to us 
to be the method par excellence of scientific investigation, 
the method of discovery, the genuine source from which all 
knowledge comes. For the popular consciousness, then, the 
two methods are sharply distinct and even opposed. 

For the scientific consciousness, on the other hand, they are 
at the present day recognised as working hand in hand, and 
indeed as a method of investigation deduction tends to be 
preferred, at least in the more advanced and exact sciences.2 
The popular view rests upon the idea that for deduction, the 
law which forms its starting-point must have been already 
established, whereas for the scientist the most fruitful char- 
acteristic of deduction consists precisely in the fact that its 

i Cf. Goblot, TraiU de Logique, pp. 82-83. 

2 Cf. Wundt, Logik, 3e Auflage, Vol. II, p. 31. 

283 



284 INDUCTION AND DEDUCTION 

starting-point may equally well be a provisional hypothesis, 
assumed deliberately for purposes of experimentation. For 
the scientific consciousness, then, the old and sharp distinc- 
tion of function which the popular consciousness still retains, 
has broken down, and it is conceivable, since both methods 
are found to work together in science, that they may not be 
so sharply distinct as is usually supposed. 

The problem of the present chapter is to examine the rela- 
tion of induction and deduction to one another, in order to 
discover whether they are two distinct methods, as the popu- 
lar consciousness and even many scientists still suppose, or 
whether they are two correlative aspects of a 'single method 
of scientific investigation, as perhaps a majority of scientists 
and logicians at the present day tend to believe. We shall 
begin by inquiring whether induction necessarily involves 
deductive elements, and shall then pass on to the question 
as to whether deduction necessarily involves inductive ele- 
ments as an integral portion of its method in investigation. 

Does Induction Involve Deduction? — Let us examine a typ- 
ical case of induction. We recognised provisionally two main 
types of induction, in the former of which abstraction seemed 
more prominent, while in the latter greater emphasis seemed 
to be laid upon determination. Subsequently, we threw doubt 
upon any attempt to draw a hard and fast distinction between 
these two types, but for the sake of completeness we shall 
here examine cases from each group. Let us consider first 
a case which belongs more to the abstraction-type. The prob- 
lem being to discover whether there is, in point of fact, a 
law of "general intelligence" pervading our activities in dif- 
ferent fields of work, we proceed by selecting a great variety 
of experimental tests, designed to probe our processes of 
attention, memory, reasoning, etc., and giving these to a group 
of subjects whose ranking, in respect of intelligence, is 
already ascertained, at least in part, by other means. Let 
us assume that the ascertained order of the subjects is A, B, 
C, D, . . . , and that the results of our experiments are 
as follows: 



No. of Test. 


1 


2 


3 


h 


5 


6 


7 


8 


9 


10 


Order of Subject A 


2 


1 


1 


1 


1 


1 


1 


2 


1 


1 


B 


4 


3 


6 


3 


2 


2 


2 


1 


3 


2 


C 


7 


5 


3 


9 


3 


3 


5 


3 


2 


3 


D 


6 


4 


4 


8 


8 


7 


6 


6 


7 


4 



INDUCTION AND DEDUCTION 285 

These figures represent the work of the preliminary anal- 
ysis and synthesis. We proceed to abstract and determine 
the final ranking of the subjects by abstracting the average of 
the # various test-results for each subject, and then arranging 
the subject accordingly. In the end, we find that our con- 
clusions agree with the previously ascertained order. Our 
tests also rank the subjects in the order A, B, C, D, . 
That is to say, the subject who is considered most intelligent 
by other standards really leads in most of the tests, and the 
subject who is considered poorest really is last in most of 
the tests, etc. So far, then, as these particular tests go, it 
looks as though there might conceivably be some such entity 
as "general intelligence" manifesting itself in solving prob- 
lems of any and every kind. 

Does deduction play any part in the above inquiry? Yes, 
it certainly does. We deduce that general intelligence — 
assuming that there is such a thing — must be such as to make 
its possessor do well in any kind of test. That is to say, we 
deduce the specific consequences, that A — supposed to be the 
most intelligent subject — will come out first in test 1, in 
test 2, in test 3 . . . , that the least intelligent subject 
will come out last in test 1, in test 2 . etc. It is 

because our experimental results on the whole bear out these 
deductions, that we consider it reasonable, so far as this evi- 
dence goes, to suppose that there may be such a thing as 
general intelligence. That is to say, without some such deduc- 
tions, we should not be able to establish or even to reject the 
suggestion. For even if the results had not borne out our 
deductions, but had led to negative conclusions, the deduc- 
tion would still have played an essential part. It is, in fact, 
only by reference to consequences deduced from an assumed 
principle, that we can be sure that the facts establish a law, 
or reject it, or leave it not proven. Deduction, then, is an 
essential and integral part of the inductive method by means 
of which we establish laws. 

Let us take another example, in which the determination- 
aspect is more prominent than the abstraction-aspect. In 
playing the piano, or in writing with a type-writer, we are 
able to estimate certain spatial relations with great accuracy, 
as is shown by the way in which we can strike almost any 
key we wish, without looking at it. What is the principle or 
law underlying this accuracy? W T e can investigate the ques- 



286 INDUCTION AND DEDUCTION 

tion by first constructing a mental model in its general out- 
lines, and then working out its details and seeing how these 
compare with the experimental results. Accuracy in motor 
localisation must depend upon something in our sense-organs. 
We must have some sensory organ capable of estimating spatial 
movements with accuracy. In the case of the arm, there are 
only three possible factors — (1) the skin, (2) the muscles and 
tendons, and (3) the joints at wrist, elbow, and shoulder. We 
assume that if one of these plays a great part in such local- 
isation, treating it in such a way as to paralyse it for the time 
being will interfere with our accuracy, and conversely, if 
throwing one of these factors out of gear makes no appre- 
ciable difference to our accuracy, it is not seriously con- 
cerned in our estimation of movement. Thus if the skin is 
sprayed with ethyl chloride, it becomes frozen, and its sen- 
sitivity is much impaired. If the skin is a vital element in 
estimating movements, we should expect our accuracy to 
diminish, and conversely, if our accuracy does not diminish, 
we should regard the skin as not playing an important part 
in such localisation. That whose presence or absence makes 
no apparent difference to the phenomenon, cannot be causally 
connected with the phenomenon. Similarly with the muscles 
and the joints. Experiments are devised which impair the 
sensitivity of one of these factors for the time being, and 
our accuracy is tested in the same way as with the skin. 
It was discovered by experiments of this type that the mus- 
cles play a certain part, but not a very great one, and that 
the chief part is probably played by the joints. 3 That is to 
say, the experiments bore out certain of our expectations, and 
refuted others. 

In such cases there is no necessity for minute inquiry. We 
very obviously deduce the consequences of our assumed 
hypothesis, and this is, in fact, often referred to as a portion 
of the "deductive method of induction." So far, then, as 
the determination-type of induction is concerned, we may 
regard it as admitted that it is fundamentally deductive. 
We may also note that a precisely similar deduction of the 
consequences of a mental model plays a part also in the 
abstraction-type. We there deduced what consequences should 

3 Of. Goldsciheider's paper in Archiv. fur Anatomic und Physiologic, 
1889, pp. 369, 540. Also James. Principles of Psychology, Vol. II, 
pp. 189 ff. 



INDUCTION AND DEDUCTION 287 

hold good if the theory of general intelligence was to be 
upheld. That is to say, we made explicit which was logically 
involved in such a theory — viz. that A would be first in tests 
1-10, etc. If such cases may be regarded as typical, our con- 
clusion is, that induction as such necessarily involves the use 
of deduction, as an essential part of the method of discover- 
ing laws. 

Does Deduction Involve Induction? — Goldscheider's experi- 
ment with the skin, muscles, and joints illustrates the deduc- 
tive method of induction, and in dealing with that aspect of 
deduction which is found useful as a method of investigation, 
it would be difficult to find a more typical case of deduc- 
tion. The use of deduction, in actual practise, is to construct 
in its details a mental model already constructed in general 
outline — to deduce the detailed consequences which follow 
from the original plan — in order to see how these compare 
with the experimental or observed results. If the two coin- 
cide in detail, the principle exemplified in the mental model 
is regarded as so far established. In Euclid's well-known 
proof of Bk. I, prop 4, the method of superposition is 
employed. The deductive element in this method consists in 
the argument that if the triangle ABC is superimposed upon 
the triangle DEF, so that the side AB falls upon the side BE. 
and the side AC upon the side BF, the plan of structure is 
such that B must coincide with E, and C with F, and the base 
BC must — as a further deduced consequence — coincide with 
the base EF, so that the triangles will be found to be equal 
in all respects. The establishment of the principle consists 
in experimenting by means of superposition, and finding that 
the experimental result does actually bear out the conse- 
quences, in proportion as it is carried out correctly, — and 
indeed cannot do otherwise. So too in the cause-effect model, 
we reason that when, if A is present X is always present, and 
if A is absent X is always absent, and if X is present A is 
always present, and if X is absent A is always absent, — then 
A and X are causally connected. These specific deductions 
represent in fact the detailed nature of the cause-effect 
mental model. Whether causal connection is or is not estab- 
lished in a particular case, depends on whether the experi- 
mental or observed results coincide with the details of this 
model, or fail to coincide, respectively. 

In scientific investigation, then, induction always contains 



'288 INDUCTION AND DEDUCTION 

deduction of consequences as a part of the inductive discovery 
of laws. But does deduction always necessarily contain 
induction? Can we perhaps maintain that induction con- 
nects up a mental model with the facts, and thus comes into 
play only when we go beyond the mental model and try to 
bring it into contact with something which is not a mental 
model — the actual objective phenomena? If so, it looks as 
though when thought was merely concerned with itself, we 
might have a deduction of consequences without the slightest 
reference to the world of natural phenomena — i. e., a case of 
pure deduction, unmixed with anything empirical and induc- 
tive. It is sometimes thought that Euclid's reasonings are of 
this kind. Can we do this, or is it impossible? 

Let us consider the actual facts. In the first place, if this 
were possible, should we not have a case of "pure" thought — 
of thought thinking itself without reference to the sense- 
perceivable world? But this is the kind of thought sometimes 
attributed to infinite Beings — i. e., is a transcendent mode of 
thought which human beings do not seem to possess. In the 
second place, we find that it is at least possible to use induc- 
tion in dealing with mental models — as when we are seeking 
to discover the key to a cipher, or to make our way into the 
puzzle box, or to solve a geometrical or algebraical problem. 
And in th£ third place, if we examine the mathematical and 
causal models exemplified above, we find that there is an 
inductive element which appears essential to the deduction 
itself, so far at least as that deduction constitutes a method 
of investigation. In the case from Euclid, the inductive por- 
tion of the method consists in the experiment of superposition 
itself, and in seeing that when the triangle ABC is superim- 
posed upon the triangle DEF, they do in fact coincide. Inci- 
dentally, in the deduction of each individual consequence 
there is involved a reference to the actual construction of the 
figure, and the verification of this reference is certainly induc- 
tive in nature. When we apply the side AB to the side BE 
so that the point A falls upon the point D, induction is 
needed to verify the deduced consequence that the point B 
coincides with the point E, and so also with the other deduc- 
tions. To each deduction of consequences there is a corre- 
sponding induction, and in fact we always proceed in this 
double way, comparing the mental plan with the actual 
details, and the actual details with the mental plan. So too 



INDUCTION AND DEDUCTION 289 

in applying the causal model, both in respect of its nature as 
a model, and in respect of its application to the world of 
events and processes in time. So far as the model itself is 
concerned, each deduced consequence is accompanied by an 
induction which verifies it, and so far as the application to 
the empirical world is concerned, so well is it known that for 
each deduction there is a corresponding induction, that the 
causal model is frequently taken as the typical model which 
represent inductive procedure, and in fact is often regarded 
as though it belonged exclusively to induction. If these exam- 
ples may be regarded as typical, then we can state that every 
deduction, as such, is necessarily accompanied by a corre- 
sponding induction which verifies and confirms it — that is to 
say, deduction necessarily involves induction. 

The Inductive-Deductive Method. — Induction and deduction, 
then, necessarily involve one another, and thus turn out to be 
two aspects of a single fundamental method of investigation. 
In the first place, they are two aspects, correlative but dis- 
tinct. In respect of starting-point, conclusion, and method, 
one special aspect stands out more prominently in the case 
which we call induction, and the other aspect is more promi- 
nent in the case which we call deduction. In induction we 
appear to be starting from an analysed and determined situ- 
ation, and to conclude to a law. In deduction we appear to 
start with a law, and to conclude with a group of conse- 
quences which together constitute an analysed and deter- 
mined situation. But these differences are only apparent. 
The appearance arises from one-sided emphasis, and if we 
look a little more closely into induction we see that it starts 
just as much with a mental model, provisionally assumed as 
incorporating the law which it is sought to establish, as with 
the situation to which such a model is assumed to apply. So 
too it concludes just as much with the application, to its data, 
of a set of consequences deduced from the mental model, as 
with insight into a law. In fact, application of deduced con- 
sequences to the data is the way in which we obtain insight 
into the law. So also in the case of deduction in its use as a 
method of investigation, if we look a little more closely, we 
see that its starting-point is not just some mental model in 
general, but a specific mental model which is adapted to the 
data. That is to say, we start just as much with the data of 
the problem as with the law or mental model, and we conclude 



290 INDUCTION AND DEDUCTION 

just as much with establishing the law as with deducing con- 
sequences. And in respect of method, we see that (1) viewed 
as inference from law to consequences it may be called deduc- 
tive, but viewed as verifiable consequences, as consequences 
legitimately inferred from the model in question definitely 
applying to the data, there is an inductive reference to the 
detailed features of the situation. In other words, the method 
has both an inductive and a deductive aspect, and these are 
thus two correlative and interdependent aspects of a method 
which is, however, fundamentally one. 

The function of the inductive-deductive method is, to sum 
up and carry through the work begun by analysis and synthe- 
sis, abstraction and determination. In fact these three 
methods, (1) analysis-synthesis, (2) abstraction-determina- 
tion, and (3) induction-deduction, may be regarded as three 
successive stages or phases of one and the same general 
method — the method of scientific investigation. In the first 
place, they are successive. Analysis and synthesis are pre- 
liminary methods, and are content with being able to take 
apart and put together again the problem under investigation, 
which is usually a concrete situation. Abstraction and deter- 
mination are more advanced methods, and, starting with a 
situation already analysed and synthesised, single out some 
element or aspect for special consideration, and by thus con- 
centrating their activities in a single direction, are enabled 
to go further than was possible for analysis and synthesis. 
At the same time, they do not go so far as induction and 
deduction, but are satisfied if they take a single element out 
of one context and determine it by reference to another con- 
text. Induction and deduction are highly complex methods 
which make use of both the foregoing methods and carry their 
work further until we succeed in discovering some law and 
its application to a situation which has been analysed and 
determined. 

In the second place, these methods are not merely succes- 
sive, but are also phases of one and the same fundamental 
method, the method of scientific investigation. This we can 
realise from the following considerations: — (1) Analysis and 
synthesis involve, as we saw, insight into the law of the phe- 
nomenon to be analysed and synthesised. So too with 
abstraction and determination, while induction and deduction 
are concerned with insight into the same law. (2) The aim 



SCIENTIFIC INVESTIGATION 291 

of all three methods is one and the same — viz. objectivity 
and completeness. They are concerned with the same objects, 
for all alike are trying to bring us into contact with the world 
in which we actually live. (3) Finally, the method is funda- 
mentally the same. In all three cases we proceed by the con- 
struction of mental models and their application to the facts 
of the situation. 

Summary — Scientific Investigation. — There is thus one fun- 
damental method of scientific investigation, in which we have 
distinguished three phases, (1) the analytic-synthetic, (2) the 
abstractive-determinative, and (3) the inductive-deductive. 
The function of this method is to enable us to understand the 
world in which we live, and to understand it objectively — 
i. e., in its own nature — and as completely as is possible for 
us. This function is accomplished by the construction of 
mental models which we can fully understand, and their appli- 
cation to the special problems and situations which arise for 
us. A perfect application of our mental models to natural 
phenomena is not quite possible. There is always a certain 
incompleteness, a gap of some sort between the rational 
model and the actual concrete situation. But the gradual 
progress of science gives us assurance that by the continued 
and persistent application of this method — i. e., by treating 
phenomena as if they were entirely rational and entirely 
resembled, at least in principle, our mathematical and other 
models — we can work our way towards a progressively morw 
objective and more complete insight into the nature and work- 
ings of the world in which we live. 

FOR FURTHER READING 

B. Erdmann, LogiTc, (2nd Edit.), pp. 742-754, 774-784. W. R. 
Boyce Gibson, The Problem of Logic, pp. 326-327. J. G. Hibben, 
Logic, Part II, chapter i. H. Lotze, Logic, Bk. II, chapter vii. Chr. 
Sdgwart, Logic, Vol. JI, pp. 418-460. 

EXERCISES 

Point out the necessary inter-relation of inductive and deductive 
aspects of the method of scientific investigation in examining the 
following cases : ( 1 ) The psycho-analytical examination of a hysteri- 
cal patient. (2) The value of circumstantial evidence in a criminal 
case. (3) Testing the accuracy of a chronoscope. (4) Studying the 
effects of alcohol upon quantity of muscular work. (5) Learning to 
sing, or <to play upon some musical instrument. (6) Studying how 
far Shakespeare followed the details of his "sources." 



CHAPTER XXVII 
DEFINITION 

The Problem. — What are our habitual beliefs on the subject 
of definition? In the first place, we feel sure that for pur- 
poses of clearness in exposition, whether in discussion or in 
writing, it is well to have the exact signification of our terms 
laid down beforehand, and to use our terms only in the sense 
thus established. We feel that language is misleading, in 
that one and the same word is usually associated with many 
meanings, a, h, c, and that a speaker may intend sense a, but 
the hearer may understand in sense b or c. The misunder- 
standings which thus arise are sufficiently annoying, where 
they are not merely amusing, in ordinary social intercourse. 
But in scientific discussions, we feel sure, such variations of 
meaning are not to be tolerated. Each science thus tends to 
develop a technical language of its own, in which an endeavor 
is made to use each term only in one sense, and in order to 
have it known what that sense is, it is usual to fix it by an 
arbitrary definition. Carried to the extreme logical conclu- 
sion to which this feeling of ours points, science should estab- 
lish an entirely artificial and technical system of signs — such 
as we find, e. g., in algebra — in order to express its thoughts 
in a way which should be unmistakable. That is to say, our 
feeling for the necessity of clearly defined terms leads logic- 
ally to the creation of a special scientific language — to what 
has been called an algebra of thought. Among thinkers, a 
number of attempts to create this symbolic language have 
been actually made, and there is no doubt that, with all their 
artificiality, they give expression to a natural tendency of our 
thought when it is dealing with problems of exposition.! 

In the second place, we have at the present day a certain 

i In the history of thought, this attempt is associated especially 
with the names of Raymond Lully, and of Leibniz. But in modern 
times, symbolic logic furnishes an excellent example, and for general 
philosophical purposes the construction of a technical terminology is 
advocated by Professor Love joy, in his presidential address to the 
American (Philosophical Association. See Philosophical Review, Vol. 
XXVI, 1917, pp. 123-163. 

292 



NATURE OF DEFINITION 293 

mistrust of definitions, even in the more abstract and tech- 
nical sciences. We think of definition as somehow interfering 
with the life and movement of thought, as crystallising it into 
clear-cut forms which, with all their clearness, are devoid of 
life. We think of definition as somehow implying that the 
movement of thought has come to an end, and as constituting 
a check upon further development. It is unprogressive, and 
stands for mental stagnation. We think of it as a creation 
of mind which has somehow come to stand between us and 
the actual phenomena which it was originally designed to 
represent — a something which hinders rather than aids the 
pursuit of knowledge. From this viewpoint, then, we tend 
to regard exact definitions with considerable mistrust, and to 
feel that they are superficial. They may be clear, but they 
do not go far into their subject, and we tend to regard their ' 
function as, at best, provisional only. 

There is, then, in our ordinary educated thinking, a certain 
confusion of ideas on the subject of definition. On the one 
hand, we tend to view it as extremely valuable, and on the 
other, we seem to regard it as almost harmful, from the stand- 
point of scientific exposition and scientific discovery. The 
problem of the present chapter is to study the subject of 
definition more closely, with a view to discovering what its 
uses are, and thus to remove the confusion in our ordinary 
ways of thinking. 

Nature of Definition. — What exactly is definition? It is a 
statement of the nature of some subject under discussion. In 
the first place, it is a statement, a mind-made structure or 
mental model, of the subject of discourse. Thus a name, or 
any sort of designation which is fixed by the mind so as to 
refer to the subject of discourse, partakes of the nature of 
definition. "The subject before you is a pencil. It is used 
for drawing and writing. It is made of a hollow wooden 
cylinder with a lead core." Each sentence here contains a 
different sketch or mental model, and is so far to be regarded 
as a definition. 

In the second place, it states the nature of a subject. It is 
an answer to the question "What is it?," or "What is its 
nature?" In the example just given, the first attempt at 
definition states merely that it is a thinkable and namable — 
i. e., a subject of discourse. The statement of the name does 
not go very deeply into the nature of the pencil. The second 



294 DEFINITION 

attempt defines it in terms of use, i. e., treats it as a usable, 
or as something whose nature is to he understood by reference 
to the system of human purposes. Its nature is declared to be 
instrumental. It is a tool for drawing or writing. The third 
attempt defines it in terms of the material out of which it is 
composed, and also in terms of structure — a lead core sur- 
rounded by a wooden cylinder. These are three attempts to 
state the nature of the object in question, and are so far 
definitions. Let us take another instance. "This object is 
called grass. It is used for feeding cattle— and indeed for a 
hundred other purposes. For the botanist it is one thing, for 
the artist it is another, for the child it is another, and for 
the moralist it is yet another thing. It is not made, but grows 
from seed in the following, way. ... It belongs to the 
genus called poa. It is a monocotyledon." In this example, 
the object, not being an artefact, does not seem to have a 
single nature. The botanist frames one mental model of it, 
the farmer another, and the moralist yet another. And there 
can be no doubt that, from his special viewpoint, each is 
justified. 

In the third place, it is some subject which is under dis- 
cussion, which we define. We do not form a mental model of 
the thing as it exists in itself, but rather of some aspect of it 
which interests us. In fact it is doubtful how far objects have 
what we could call a "nature" in themselves. What we define 
is always their nature in reference to some interest or purpose 
of ours. That is to say, our definitions have not only an 
objective, but also a subjective reference. For example, it is 
usually possible, given a number of definitions of one and the 
same object, to infer to the interest or purpose behind the 
definition. Thus, take the three definitions of Grass: — (1) the 
natural food of sheep and oxen, (2) the English equivalent 
of the Latin poa pratensis, (3) a species of the genus poa, 
tribe festuceae, family gramineae. It is easy to see that the 
first is a farmer's definition, the second a scholar's, and the 
third a botanist's definition. Definition, then, has a subjective, 
as well as an objective reference. 

Aim of Definition (A) Objectivity. — Definition thus pre- 
sents us with a mental model of some object in relation to 
some interest of ours. What is our aim in framing such 
mental models or statements? In the first place, we aim at 
objectivity. We wish to represent the actual nature of the 



AIM OF DEFINITION 295 

object in which we are interested. To say that definition 
has a subjective reference, does not in any way invalidate 
this statement. It is true that it is from his own point of 
view that the farmer is interested in grass. But from that 
point of view he wants to know what grass is. The point of 
view does not swallow up the difference between natural and 
artificial feeds, or between one sort of feed and another. On 
the contrary, the special viewpoint leads to special refine- 
ments of insight into the nature of the subject under dis- 
cussion — such as studying the chemical properties of grass 
which render it especially nutritive to cattle. It leads to 
analysis and synthesis, abstraction and determination, and 
may result in a considerable accession of knowledge. So too 
the student who is translating from Latin into English does 
not care whether poa is monocotyledonous or dicotyledonous, 
whether sheep feed on it or not — all he wishes to know is, 
by what English word it is best translated. But this he does 
wish to know, and wish to know correctly. The scholar's 
viewpoint, too, may lead to all kinds of refined and subtle 
research. The taking a special viewpoint, then, does not 
interfere with the search for objectivity, but on the whole 
rather assists it by concentration of effort in a special direc- 
tion, and we can fairly say that our primary aim in defining 
is objectivity, or getting in touch with the real nature of the 
object under discussion. 

(B) Completeness. — In the second place, we aim at com- 
pleteness. We aim at so defining or stating the nature of the 
subject of discourse, that, from the viewpoint which interests 
us, nothing remains to be added, and nothing is to be taken 
away. Whatever the special question which definition asks, 
we aim at answering that question completely. Thus in the 
case of poa pratensis, the scholar's "What is it?" means, 
what is its correct English name?, and the complete answer 
to his question is contained in the word Meadow-grass. What 
we wish to avoid in definition is vagueness, indefiniteness, 
ambiguity, incompleteness in any shape or form. We want 
to be definite, precise, exact, clear, final. We want our 
definition to accomplish what it sets out to do. We want it 
to be complete. 

How Far Realisable? (A) With Mind-made Entities — 
How far can we express the nature of some subject in which 
we are interested, in a way which shall be both objective and 



296 DEFINITION 

complete? Let us consider first the case of mind-made 
entities. "A chair is a piece of furniture designed for a single 
person to sit on. A chair is made of: — 4 legs, with supporting 
cross-pieces, 1 seat, 1 back, and possibly 1 or 2 arms. These 
materials are put together in such a way that the legs are 
fastened to the seat from beneath, and the arms and back 
from above, in this manner. . . ." Here we have three 
definitions of a mind-made object from the viewpoint (1) of 
function, (2) of materials, and (3) of structural plan. All 
three definitions are objective. For, in spite of the difference 
of viewpoint, each expresses the actual nature of the object 
from its special angle of approach. Thus, the function of a 
chair is to be sat upon, and to be a piece of furniture. That 
is what Aristotle would call its final cause, the idea which we 
seek to realise in constructing chairs. So also the materials 
out of which it is to be put together are legs, seat, back, etc., 
just as much as the ''Two N's, two O's, an L and a D" are the 
materials out of which the name London can be put together 
This is what Aristotle calls the material cause of the chair. 
So also in the case of structural plan. If the materials are 
put together in accordance with the directions, we do actually 
have a chair. This is what Aristotle calls the formal cause. 
If Aristotle's viewpoint is here accepted, each of these 
definitions will be seen to belong to the causal type of mental 
model, though, in respect of the last two, mathematical 
aspects also enter in. In dealing, then, with artefacts, our 
definitions can be objective. 

Can they also be complete? "A piece of furniture designed 
for a single person to sit upon" — is this a complete definition 
of a chair? Complete, that is, from its special standpoint? 
We can test its completeness by asking (1) are all chairs 
pieces of furniture designed with this purpose, and (2) are 
all pieces of furniture designed for a single person to sit 
upon — chairs? (1) seems to be correct enough, but (2) seems 
to include stools as well as what we should call chairs. 
However, if what we are interested in is not structure, but 
function, even (2) is correct. For the difference between stool 
and chair is chiefly structural. From the special viewpoint, 
then which is interested in function, our definition may be 
regarded as complete. So too in the case of the other two 
definitions. (1) All chairs are constructed out of material 



AIM OF DEFINITION 297 

such as legs,2 a seat, a back, and possibly arms, and (2) all 
objects constructed of such materials are what we should call 
chairs. So too (1) all chairs are constructed in accordance 
with the plan mentioned, and (2) all objects constructed in 
accordance with such a plan would be called chairs. In deal- 
ing with artefacts, then, our definitions can be regarded, not 
only as objective, but also as complete, at least, from the 
special standpoint of each definition. 

Let us take another example. "A triangle is what one learns 
to construct in a special form in the first proposition of the 
first book of Euclid. A triangle is a three-sided rectilineal 
closed figure. A triangle consists of three angles which 
together form a closed figure. A triangle is a rectilineal 
closed figure, the internal angles of which are together equal 
to two right angles. A triangle is a rectilineal closed figure 
such that any one of its external angles is equal to the sum 
of the interior opposite angles. Etc., etc." 

Each of the above definitions is objective. The construction 
of a triangle is the subject treated of in Euclid I. i, a triangle 
is a three-sided figure, a three-angled figure, and does possess 
all the other properties ascribed to it, along with very many 
more which might equally well have been used, and no doubt 
many of which have not yet been discovered. Of the objec- 
tivity of all of these definitions, there can be no possible 
doubt. Are they, however, all complete? Let us consider? 

(1) All triangles are what we learn to construct in a special 
form in Euclid I. i. — Yes, for we there do learn to construct 
the equilateral form, to construct any equilateral triangle. 

(2) All things which we learn to construct in the special form 
according to Euclid I. i, are triangles. — Yes, this also is true. 
All equilateral triangles are certainly triangles. The first 
definition, then, appears to be complete. Again, (1) all 
triangles are three-sided rectilineal closed figures, and (2) all 
three-sided rectilineal closed figures are triangles. The second 
definition is complete, and the same proves to be the case 
when we apply the same test to the others. If the above 
examples may be regarded as typical, then, we can state that 
in respect of mind-made entities our definition can be both 

2 The number of legs is relatively immaterial. We think of most 
chairs as possessing four legs. If, however, it is thought advisable 
to point out that some chairs have only three legs, and are still perfect 
as chairs, it is easy to alter the definition, by specifying the possible 
variation in the number of legs, as of arms. 



298 DEFINITION 

objective and, from its special viewpoint, complete. This is 
especially recognised in the case of equations. An equation 
is recognised as the complete definition of the corresponding 
graph, and the corresponding graph might equally well be 
regarded as the complete definition (from a certain viewpoint) 
of the equation.3 

(B) With Natural Phenomena. — As we have seen, we 
deal with natural phenomena through the medium of mental 
models, and thus our definition of a natural phenomenon is 
the mental model itself, in terms of which we are trying to 
understand the phenomenon in question. As there is, further, 
a gap which separates our mental model from the natural 
phenomenon, there can be no doubt that our definitions are, 
directly, statements of something different from the object to 
be defined, and refer to the object itself only indirectly. Thus, 
when we define an island as "a piece of land surrounded by 
water," we are directly constructing the mental model of a 
circle — or of some such geometrical outline— and we can only 
apply this mathematical model to the natural phenomenon 
by a kind of mental flat — "Let one side of this figure be 
regarded as land, and the other as water." If we change the 
direction of this flat, and regard the outside as land, and the 
inside as water, we have, with the same geometrical model, 
the definition of a lake. At the same time, although there is 
thus a gap between the mental model and the reality — a gap 
which has to be bridged by this flat, a certain degree of 
objectivity cannot be denied to such definitions. If we define 
an island as "a hill-hop from the sea-floor projecting in part 
above the water-level," we seem to be a little more nearly 
expressing its objective nature. So too in Zoology it is usual 
to define the spider or the horse in terms of the mental model 
of family relationship. In such cases, while there is no 
doubt that this specific model has an objective application, 
reference to a number of authorities will show that opinions 
differ as to what animals should be assigned to the arthropod 
or mammal group, and even to the invertebrate and vertebrate 
groups. From this evidence it would appear, that, so far as 
the concrete filling in of this mental model is concerned, we 
can hardly expect full objectivity. Still, there is no doubt 
that such definitions are partly objective, and that, as science 

3 Cf. Goblot, Traite de Logique, pp. 121-122. 



TYPES OF DEFINITION 299 

advances, definition of natural phenomena can become progres- 
sively more objective. 

So also in respect of completeness. The work of science is 
never complete, and consequently the summing up of our 
knowledge at a definite stage, and its embodiment in a defini- 
tion, can never be fully complete. In respect of completeness, 
then, as well as of objectivity, the aim of definition can in 
such cases be only approximately and progressively realised. 

Types of Definition. — The general question of definition 
is "What is it?" To this question certain typical forms of 
response are given by certain typical forms of definition. 
Let us consider a few of the more prominent forms. In the 
first place, definition means, laying down the fines or bound- 
aries of a subject, establishing its outlines in such a way as 
to distinguish it from all other subjects with which it might 
be confused. For example, "Pages 387-419 of Pillsbury's 
Fundamentals of Psychology" is an exact preliminary defini- 
tion of an assignment on the subject of Reasoning — a state- 
ment of the boundaries of the subject to be studied, which is 
perfectly adequate to distinguish it from being confused with 
any kindred subject. So too, "all books numbered 160-199" is 
an exact preliminary definition of the books on philosophy in 
the Minnesota University library. It lays down the precise 
boundaries within which such books will be found, and serves 
to distinguish philosophy books from books on psychology — 
which are numbered 150-159— with all the precision to be 
expected in a library. For assistants in the library, and for 
such students as have access to the stacks, such definitions are 
not only useful, but also for many purposes perfectly adequate. 
For certain purposes they are not only needed, but are all 
that is needed. 

What exactly is this kind of definition? It is not, of course, 
the object, but is rather a kind of outline sketch or model of 
its boundaries. It is even of a mathematical character, and 
indeed derives much of its exactness from the use of numbers. 
Its function is to localise the object with which we wish to 
get in touch, and it has even a directly spatial reference. 
This is true not only in such cases as "The third house on 
your right after you have crossed the park," as a definition 
of the locality where Mr. X lives, but also of the portion of 
the text-book set for a lesson on Reasoning, and even in the 
case of the philosophy books — for the numbers have a very 



300 DEFINITION 

definitely spatial reference to certain shelves located in a 
certain room of the library. Such a definition tells us, not 
exactly what the object is, but rather where it is to be found. 
It is a mathematical model with a spatial reference. 

Let us consider a second type of definition. "A pencil is 
something used for writing, when there is no ink. A type- 
writer is something you use when you want to write as 
clearly as print. A spoon is something you use for stirring 
liquids, or for eating food like soup or oatmeal. A meal is 
what you take to satisfy hunger. A dog is what you use to 
guard the house from tramps. Art and religion are the most 
ennobling things we have in life." For certain purposes, 
especially practical purposes, there can be no doubt that such 
definitions are perfectly adequate. They are sketches of the 
objects in terms of use, and thus refer partly to the nature 
of the object, and partly to the system of human purposes. 
On the one hand, they tell us what the object can be used for, 
and on the other, they tell us how we can use it. They are 
thus mental models of the objects under discussion, in terms 
of human uses, and as such are of the greatest importance to 
practical men. 

There are many other types of definition. Thus, certain 
definitions refer less to what we human beings can do with 
the object, and more to what it itself does in a state of 
nature: — "A fire is something which burns. Water is some- 
thing which flows, and wets whatever falls into it. Rain is 
something which comes down from clouds in the form of 
drops of water — is something which helps to make the crops 
grow, especially in the spring-time." This is a kind of causal 
model, and tells us what the object does. Another type of 
causal model tell us rather how an object is caused or pro- 
duced: — "Thunder is a phenomenon due to lightning. Plant- 
rust is a phemonenon due to the action of bacteria. A rain- 
bow is a phenomenon caused by our seeing the sunlight 
through water." 

The typical forms of definition meet the general question 
"What is it?" by answering questions such as "Where is it, 
What can we do with it, What does it do, or make, or cause, 
How is it caused, or made, or produced, What is it made of, 
What is its law or principle of construction?" There is no 
limit to these questions. Each expresses a different interest, 
or represents a different angle of approach, and there are as 



VALIDITY OF DEFINITION 301 

many possible types of definition as there are possible inter- 
ests, or possible questions to be asked. As these are indefi- 
nite in number, and have never been classified, it is profitless 
to attempt to limit definition to any one form — as has been 
attempted in the history of logic. Any definition which 
answers its special question in a way which is objective and 
reasonably complete, represents a legitimate type of defini- 
tion, and no definition absolutely exhausts the full nature of 
its subject. 

Validity of Definition. — Definitions are mind-made entities 
in terms of which we try to understand the world around us. 
There is thus something experimental about them. They 
enter into the method of trial and error, and are frequently 
mistaken and thus false. In point of fact, this is true when 
we are defining mental models themselves, as well as in the 
case of natural phenomena. Thus, a common dictionary defi- 
nition of a triangle is "A figure with three angles. "i But if we 
test this by asking, are all figures with three angles triangles? 
we see at once that it is inadequate. For we might have an 
open figure, like a square with one corner missing — which 
would certainly be a figure with three angles, and would with 
equal certainty not be a triangle. So too a common dictionary 
definition of chair is "A movable seat." 1 But strip a chair of 
its legs and back, and it is still a movable seat. So also a 
stool or bench might be called a movable seat. But none of 
these would be called chairs. In the case of natural phenom- 
ena, it is not necessary to give specific instances. For as the 
history of science shows, all definitions of such phenomena are 
incomplete, and very many, if not all, are also partially false. 
Definitions, then, may be invalid. On what does their validity 
or invalidity depend? 

In the case of mind-made entities, where the object may be 
created by mental construction, it is possible for a definition 
to be perfectly valid. Thus we can define the knight's move 
or bishop's move in class with perfect accuracy, or "Align- 
ment" and "Point of rest" in military science, provided that 
we follow the established conventions. So also in the case of 
triangles and other mathematical objects. If we accept the 
general view of mathematical space, we can define with suffi- 
cient accuracy. Mistakes are made here from time to time, but 

1 The definitions here are taken from The American Popular Dic- 
tionary of the English Language. 



302 DEFINITION 

they can be rectified, and made satisfactory in point of objec- 
tivity and completeness. In the case of natural phenomena, 
however, complete validity is out of the question. But our 
definitions can, even in such cases, approximate to validity as 
scientific knowledge increases, and as our definition sums up 
correctly the knowledge of our own time. The only adequate 
test of such definitions is the progress of science itself. The 
further development of knowledge alone can show whether 
the views held at an earlier stage were pointed in the right 
direction or not. In general, then, a definition is valid, so 
far as from its special viewpoint it expresses the objective 
nature of the phenomenon under discussion. 

Function of Definition in Exposition. — For scientific pur- 
poses, whether of inquiry or of exposition, definition has two 
main functions. In the first place, it is used in opening up 
an inquiry, in the form of a preliminary definition. Its use 
in such cases is to establish the general lines along which 
research or discussion is to be carried on. Thus, in scien- 
tific exposition, it is usual to start with a statement of the 
"problem," or to sum up the beliefs with which we approach 
a new subject, as Coleridge, before opening a new book, used 
to write down briefly his own thoughts on the subject. Used 
in this way, preliminary definitions are found very helpful 
in dealing clearly and objectively with a subject of discourse. 

In the second place, definition is used in closing an inquiry, 
in the form of a concluding or final definition. In such 
cases its function is to sum up the results of inquiry, to 
answer the problem set at the beginning, or at least to sum up 
the beliefs with which we lay the subject on one side — as 
some thinkers write down briefly what they have learnt from 
each book they read, immediately after finishing it. Such 
concluding definitions are of the utmost value in promoting 
clearness, definiteness, and objectivity in our researches and 
explanations. 

Summary and Conclusion. — So far we have seen that defini- 
tion states, in terms of some mental model, the nature of 
some subject of discourse, and that its aim is objectivity and 
completeness. This aim can be attained in the case of mind- 
made entities, and we can at least progressively approximate 
to such objectivity and completeness in the case of natural 
phenomena. We have also seen that the chief use of defini- 
tion in scientific exposition is to open or close an inquiry, in 



VALUE OF DEFINITION 303 

the form of a preliminary, or of a concluding definition, as 
the case may be. 

We should now be in a position to resolve the difficulty 
with which our inquiry opened. Is definition a help, or is 
it a hindrance, to scientific progress? It is certainly a crea- 
tion of mind, a mental model, but its function is not to stand 
between us and the object, and thus obscure or mislead our 
vision. Its aim is to state the nature of the object, and to 
be a help towards clearing up our ideas and guiding our 
vision aright, and we can state that, in proportion as mental 
models prove of assistance to the progress of knowledge, so 
far definitions are helpful. On the whole, the preliminary 
definition seems of more assistance than the concluding 
definition — for it certainly leads to further progress. But if 
we adopt the modern progressive view of science, and do not 
regard our conclusion — the summing up of our inquiries as 
far as we have gone — as concluding the subject, and exhaust- 
ing the nature of the subject itself, we can say more. If we 
regard our concluding definition not as in any way final, but 
rather as leading on to more determinate inquiries, both forms 
of definition may be equally fruitful and equally helpful in 
scientific exposition. What we objected to in definition, was 
not its clearness but its tendency to pass over into dogmatism, 
into the idea that it was more than an experimental mental 
model, always subject to revision. If, however, we avoid this 
error, we shall find definition always of assistance in under- 
standing ourselves and in general the world in which we live. 

FOR FURTHER READING 

W. R. Boyce Gibson, The Problem of Logic, pp. 32-36. H. Lotze, 
Logic, Bk. II, chapter i. Chr. Sigwart, Logic, Vol. I, pp. 286-294. 
W. Wundt, Logik, (3rd Edit.), Vol. II, pp. 40-47. 

EXERCISES 

1. Give three definitions of each of the following, from three 
different viewpoints : Circle, Typewriter, Child, Apple, Air-plane, 
Diamond, Dandelion, Book, Ink, Student. 

2. Is there any viewpoint from which the following definitions are 
strictly legitimate: (a) A lake is a water island in the land, (b) 
A lama is a woolly sort of fleecy hairy goat, with an indolent expres- 
sion and an undulating throat. (c) A liar is a man who wilfully 
misplaces his ontological predicates, (d) A caterpillar is an emblem 
of life and a vision of joy. (e) A straight line is the arc of a circle 



304 DEFINITION 

of infinite radius, (f) A useless life is a form of death, (g) God 
is a substance consisting in infinite attributes, of which each expresses 
eternal and infinite essentiality, (h) True wit is nature to advantage 
dressed, what oft was thought, but ne'er so well expressed. (i) A 
politician is not a saint, (j) A locomotive is something which moves 
from one place to another, (k) An honest man is the noblest work 
of God. (1) Architecture is frozen music? 



CHAPTER XXVIII 
CLASSIFICATION 

The use of classification is universal. Not only in science, 
but also in every-day life, we classify everything and every- 
body. We classify a new acquaintance as someone we can 
or cannot get on with. We classify him as clever, stupid, or 
just average. We classify him as old, young, or middle-aged 
— as tall or short, thin or fat, plain or good-looking, rich or 
poor. In fact, there is no viewpoint — social, industrial, politi- 
cal, artistic, religious, etc., from which we cannot put him 
into some class, into a group along with other people. In 
science, the importance of classification for investigation, as 
well as for exposition, can hardly be over-estimated. By 
grouping together a large number of phenomena or experi- 
ences which bear upon a single point, it is usually possible 
for a scientist to obtain insight into some law, or for a 
speaker or writer to transmit his own insight to others. In 
general, then, for every-day life as for science, classification 
is of universal use. 

Nature of Classification. — Just what is classification? It 
means, quite simply, putting together so as to form a class. 
In the first place, it signifies our putting together. That is to 
say, the viewpoint from which we classify is ours, depends 
upon our interests and purposes, and is so far subjective and 
even arbitrary. For instance, to group together books on 
various subjects, in accordance with the first letter of the 
writer's surname, seems thoroughly artificial. It has very 
little to do with the nature of the book, and indeed seems 
largely accidental. There is no logical connection between the 
fact that this book, which happens to be on metaphysics, 
should have been written by a man whose family name began 
with M, and the fact that that book, which happens to be on 
metaphysics, should have been written by a man whose family 
name began with B or T. There is, in fact, no necessary connec- 
tion between the first letter of a man's surname and the nature 
of his writings. Why, then, do we group books in this way? 

305 



306 CLASSIFICATION 

It is because we find it convenient. There are only twenty- 
six letters in the alphabet we use, and we are thus able to 
assign any book whatever to some one of twenty-six recog- 
nised classes, and for purposes of reference this is found 
convenient. So too in a very small private library, it is 
quite common to find books assigned to different shelves in 
accordance with their size, so that all the smaller volumes 
go on this shelf, and all the ponderous tomes on that. This 
also has little or nothing to do with the contents of the 
books in question, but it suits the conveniences of the owner 
of the books. So too for purposes of shipping, books can be 
classified according to weight, or for esthetic purposes accord- 
ing to color and style of binding. They might also be classi- 
fied according to place of publication, according to date of 
publication, according to the name of the publisher — or accord- 
ing to any one of a hundred different interests and purposes. 
Classification, then, in the first place is arbitrary. We put 
together in accordance with our interests. 

To this arbitrariness there is, however, a limit. We put 
together only what can be put together. We do not group 
books according to their thermodynamic qualities, or accord- 
ing to their arboreal habits, or according to their qualities as 
chronoscopes, plethysmographs, or type-writers — because they 
have no such qualities. We put them together in accordance 
with characteristics which they really have. It may be acci- 
dental for a book on political economy to be written by a 
man whose family name began with M. There are books on 
political economy written by men whose names began with 
S or Y. But there is no doubt that, in that particular case, 
it does begin with M, and as we find that convenient for our 
purposes, we make use of that characteristic. In the second 
place, then, we group together in accordance with some char- 
acteristic which the object to be classified really possesses. 

In the third place, we put them together so as to form a 
class. What is a class? A class is a group of individuals 
held together by some law of connection, this law being some 
principle which all have in common. Thus students of biology 
form a class, being held together by the interest in biology 
which all have in common. Books written by men whose sur- 
names begin with M form a class, being held together by the 
characteristic which all possess in common, and, in general, 
wherever objects have a single characteristic in common, 



AIM OF CLASSIFICATION 307 

whatever that characteristic, and however superficial or acci- 
dental it may seem, such objects can be grouped together 
so as to form a class, provided always that some one happens 
to be interested in that special characteristic. 

Finally, in order to obtain a clear idea of the nature of 
classification, we must compare it with what is known as 
Division. Classification groups together individuals so as to 
form a class. Division takes a class apart, so as to form sub- 
classes. Thus, we can group individuals together as Amer- 
icans, as men interested in business, as millionaires, as 
politicians, or simply as men. This is classification. On the 
other hand, we can take the class men, and subdivide it into 
white-skinned, yellow-skinned, brown-skinned, red-skinned 
men, etc., — i. e., we can divide the class up into sub-classes 
according to variations in respect of a single characteristic. 
So too we can divide politicians into progressives and reaction- 
aries, into honest and corrupt, or millionaires into coal-kings, 
railroad-kings, etc., according to variations in respect of the 
source of their wealth. On the whole, division and classifica- 
tion should be regarded as two aspects of a single method, like 
analysis and synthesis, abstraction and determination, etc., 
and in order to grasp sufficiently the nature of classification, 
it is necessary to bear in mind this relation to division. Thus, 
in classifying individuals as millionaires, we are putting them 
into what is a sub-division of the class men, and in dividing 
the class millionaires into the sub-classes of coal-kings, rail- 
road-kings, etc., we are forming classes. Classification thus 
means, placing individuals together in a class which is usually 
itself to be regarded as a sub-class of some wider organisa- 
tion. 

1 "Classification, then, is arbitrary — in that a class is formed 
from some particular viewpoint; yet not wholly arbitrary — 
for the individuals which are put into the class all possess 
some common characteristic, in virtue of which they can be 
unified and regarded as constituting a single group; and 
finally the class w T hich we form is usually a part of some 
wider system, so that classification is a kind of organisation. 

Aim of Classification (A) Objectivity. — What do we classify? 
What is our aim in grouping together all sorts of objects 
which possess a single characteristic in common? In the 
first place, we aim at objectivity. It is with a view to hand- 
ling the objects more conveniently, and understanding the 



308 CLASSIFICATION 

objects more readily, that we form them into groups. Every 
science, and every complex research or exposition, has its 
classificatory stage, during which it is assembling material 
and getting it into usable shape. It is with the aim of getting 
into closer touch with the objective nature of this material, 
that science classifies it, or forms it into various groups which", 
for purposes of inquiry or exposition, seem to belong together. 
Thus in Botany, the otherwise enormous and unwieldy mass 
of material is grouped according to the family connections 
of the different small groups, so that the plan of systematic 
botany resembles a genealogical tree. But this classification, 
which is made primarily from the viewpoint of the evolution- 
ary theory, is in a secondary way of use for other purposes 
also, so far as it makes the material more easily handled. 
Thus, in studying the reactions of plants to stimulation, the 
new viewpoint cuts across all the old class distinctions, and 
it is necessary to form an entirely new grouping, according as 
the type of reaction to light, for instance, or to contact, sep- 
arates members of one and the same family group, and links 
them up with members from widely diverse branches of the 
genealogical tree. But until the re-grouping in accordance 
with the new interest has been effected, it is found conveni- 
ent to investigate one family group at a time, in search of 
the new characteristics, following through the standardised 
family-group plan, until the whole ground has been covered. 
So too with periodical literature. It is published in various 
magazines, each of which for purposes of reference tends to 
be regarded as forming a kind of standardised class of its 
own. But when we are interested in some single question — 
e. g., the study of apparitions — we collect together into spe- 
cial groups all articles dealing with apparitions of animals, 
apparitions of mail-coaches, apparitions of houses and gar- 
dens, etc. But until the new grouping has been carried 
through, we find it convenient to make use of the old group- 
ing in magazine-units, because in this way, by looking up 
the index of magazine A, of magazine B, etc., we can conveni- 
ently cover the whole ground, and can get into touch with 
everything in the periodical literature which bears on our 
special interest. The primary aim, then, of classification is 
to reduce the material studied to such a form that we can 
handle it conveniently, and thus bring ourselves into closer 



AIM OF CLASSIFICATION 309 

contact with the objective facts than would otherwise be 
possible. 

(B) Completeness. — In the second place, we aim at a cer- 
tain kind of completeness. We wish to cover the whole ground, 
and to leave nothing important out of account. Classification 
and division together always aim at covering the entire field. 
Division, for instance always tries to be exhaustive. We 
divide, e. g., books in general into books on history, books on 
chemistry, books on philosophy, etc., and at the end, when we 
have used up all the definite subjects of study or reference, 
we group together the remaining volumes as "miscellaneous." 
So too in classifying. If we are making a collection of all 
books bearing upon some minute point in history or literature, 
or on a subject such as porcelain or indigo-dyeing, we want 
our class to be complete. In such cases, in order to ensure 
that nothing important shall escape us, we tend to go over 
the whole ground by the aid of division, so that all standard 
groups of books — literature, history, art, etc. — come in for 
consideration, and the whole field of literature is covered. 
We do not, of course, aim at including every single book bear- 
ing on our subject, but rather one book for each distinctive 
view point, i. e., at including books each one of which definitely 
adds something new to the collection. We aim at including 
representatives of every variety, every distinct species, and 
thus to cover the entire ground in a way which shall do 
justice to its many-sidedness. 

How Far Realisable? (A) With Mind-Made Entities. — In 
grouping objects together so as to form classes, how far can 
we realise this aim of objectivity and completeness? Let us 
consider first the case of mind-made entities. Can we form 
a class of musical instruments in a way that shall be objec- 
tive and complete? Let us see. We take first of all instru- 
ments which produce musical tones by means of striking a 
vibrating cord — such as the monocord, clavicord, clavecin, 
piano, etc., then instruments which produce musical tones by 
means of pulling or plucking a cord — such as the harp, guitar, 
the whole lyre family, the spinet, etc., then instruments which 
produce the sound from cords by bowing — as the violin and 
the whole viol family — then the group of percussion-instru- 
ments — such as the drum — woodwind instruments — such as 
the flute family — reed instruments — such as the oboe, clar- 
inet, etc., on the one hand, and the harmonium on the other, 



310 CLASSIFICATION 

etc., etc. In short, by classing instruments together in groups 
according to the way in which the tones are produced 
we could try to find a place for everything. Such a class 
would certainly be objective — for it would really group 
together actual types of musical instrument — and there is also 
no doubt that it can be reasonably complete. Indeed, so far 
back as we have historical records, it can be entirely com- 
plete. 

Let us take another instance. Can we construct a class 
of curved lines which shall be both objective and complete? 
Let us see. A curve is anything from a circle on the one 
hand to almost a straight line on the other. We can put 
together a class of regular curves, composed of representa- 
tives of the circle-group — the circumference of a larger circle 
is less curved than the circumference of a smaller circle, and 
the arc of a circle of infinite radius would be a straight line 
■ — of the ellipse-group, of the parabola-group, etc., and thus 
secure a class which is certainly objective, and is reasonably 
complete — in fact, entirely complete. For although the num- 
ber of possible degrees of curvature is theoretically unlimited, 
the whole ground has been covered. So too with books, pic- 
tures, and tools of any and every sort. All mind-made entities 
can be classified in a way which is both objective and complete. 

(B) With Natural Phenomena. — We classify natural phe- 
nomena, not directly, but through the medium of mental 
models. For instance, if faced with a collection of articles so 
heterogeneous that we can bring them under no other single 
head, we proceed to make an "inventory" of them. That is to 
say, we make a list of all the articles, with the numbering 
1, 2, 3, 4, . . . — i. e., put them together in terms of a 
mathematical type of mental model. This is not perfectly 
exact, from an objective viewpoint. For on the inventorial 
list every object listed counts for one, and none counts for 
more than one, and this standard, when applied to diverse 
objects, is often a traversty. But from the view point of com- 
pleteness it leaves little to be desired, for it certainly covers 
the whole field, though in a very preliminary way. So too 
in geology we classify the various crystals in nature in terms 
of a mathematical group consisting of the tetrahedron, octo- 
hedron, dodecahedron, etc. But the mathematical group 
includes forms not found in nature, such as the eikosihedron, 
and the actual forms never perfectly correspond to the mathe- 



TYPES OF CLASSIFICATION 311 

matical models, so that, while the mathematical series is com- 
plete^ — for it certainly covers the whole possible field — it is 
not perfect in respect of objectivity. So too in chemistry the 
various elements, when arranged in relation to atomic weight, 
are found to lie on a spiral curve, and by investigating cor- 
respondencies suggested by this mathematical model, many 
important discoveries have been made. But here too, there 
are gaps, and the spiral is more perfect than the empirical 
facts which it puts together into a group. That is to say, it 
is perhaps too complete, and is not perfect in respect of objec- 
tivity. 

At the same time it must be admitted that classification of 
natural phenomena in terms of such mental models is cer- 
tainly of very great assistance in bringing us into objective 
contact with the actual varieties of natural objects, and that 
the progressive insight into the objective facts which is thus 
brought about, could probably not be brought about in any 
other way. Classification of natural objects, then, progres- 
sively approximates to objectivity, but is never perfectly 
objective. It is, however, complete, in the sense of covering 
the whole ground — that is to say, complete in a somewhat 
external way, as an inventory may be complete, whatever the 
objects thus assembled, and whether they have any inner 
relation to one another, or not. 

Types of Classification. — The most elementary type of class- 
ification is the inventory, a. simple mathematical model with 
no pretensions to going deeply into the nature of the sub- 
ject studied. Objects are simply numbered, quite arbitrarily, 
as 1, 2, 3, 4, . . . , in the order in which the classify- 
ing clerk happens to come across them. The best known 
and perhaps most frequently used of all types of classification 
is a refinement upon this. It is called index classification. 
This also is largely accidental and arbitrary, and does not 
go far into the nature of the subject. But by confining the 
number of classes to twenty-six which are grouped from A to 
Z, a great step has been taken towards introducing order and 
system. Because of its very great convenience for purposes 
of reference, this alphabetical model is used in classifying 
all sorts of objects — e. g., in filing away letters of all kinds, in 
libraries, in commercial offices, in administrative work, in 
research work, and generally, wherever it can be applied. 
There are many variants upon this principle, and we have 



312 CLASSIFICATION 

card-index systems based upon the days of the month, or of 
the week, or of the hours of the day, or of a series of years, 
etc. There is no absolute limit to its usefulness, or to the 
variations of model which may be employed. 

Another common kind of classification is the diagnostic 
type. This resembles index classification, in that it is used 
largely for purposes of reference, but at the same time goes 
somewhat further into the nature of the subject studied. The 
characteristics used for forming the groups are selected upon 
the basis of being striking and immediately evident, and thus 
tend to be somewhat external and superficial. But they are 
not so superficial as the initials A, JB, 0, ... Thus a 
physician readily classifies a disease by reference to the most 
striking symptoms, and many an amateur botanist finds out 
to what family the specimens he discovers belong, by looking 
them up in a book especially written from this viewpoint. So 
too the common way of judging character on the basis of 
general appearance and readiness in conversation belongs to 
this type, and in fact most of us carry around in our heads 
a ready-reference system of this general type, for dealing with 
any subject in which we are especially interested. 

A further type of classification, common in pure science, 
goes more deeply into the general nature of the subject studied. 
Thus, the kind of classification which we find in zoology and 
botany attempts to group together animals, or plants, accord- 
ing to their family relationships, and generally to trace their 
descent, according as the various genera and species seem to 
have developed in nature. Because biologists thus follow 
lines of organisation established by nature, this type is some- 
times referred to as natural classification, though there has 
been among logicians an attempt to extend the usage of this 
term so as to cover all cases of classification of a certain type. 
Thus classification tends to be called natural, where the group- 
ing seems to deal with the subject less from isolated and 
arbitrary viewpoints which cut across all "natural" class-dis- 
tinctions, and more from insight into some law which seems 
fundamental in explaining the various characteristics of the 
object as a whole, as the principle of evolution helps to 
explain a very great number of characteristics in biology and 
anthropology. We must admit, however, that from a strictly 
logical viewpoint this form of classification also is arbitrary; 
tor the scientist has a special interest in tracing lines of 



VALIDITY OF CLASSIFICATION 313 

descent, and to group animals in terms of mere family rela- 
tionships may be highly artificial. We see this especially 
when it comes to classing together objects whose structure is 
very different — such as (1) thriving members of a group and 
(2) degenerate parasites which are the suckers and hangers 
on of animal society, sans eyes, sans legs, sans almost every- 
thing except their great thirst and their family tree. 

If, however, we set out to classify the various typical forms 
of classification, we soon find that they are too numerous, and 
based upon too great a variety of interests, to be fully class- 
ified. Some follow structural lines, others follow functional 
lines, and many of the special models employed defy any 
general naming.' The fact is, types of classification may be, 
and should be, nearly as numerous as the interests and ques- 
tionings with which we approach the phenomena of experi- 
ence. These, however, are too numerous and too diverse to 
be classified profitably, at least at the present stage of knowl- 
edge. 

Validity of Classification. — Not all classifications are cor- 
rect. On library shelves, books are generally grouped together 
primarily in respect of content and secondarily in respect 
of alphabetical considerations. Thus, all encyclopedias are 
grouped together, and all books on logic are grouped together, 
although within the group the books written by authors whose 
surnames begin with A are placed first, etc. It so happens 
that a well-known work on logic was originally published as 
volume 1 of a projected "encyclopedia of the philosophical 
sciences." The other volumes have never appeared, but the 
volume on logic will, in many libraries, be sought in vain 
where it should be — among the books on logic, and will be 
found where it has no right to be — between two of the ency- 
clopedias. Classifications are thus sometimes incorrect. On 
what does their validity or invalidity depend? It depends 
solely upon whether they serve their special purpose, and 
help us to understand the objective nature and objective con- 
nections of the phenomena studied. Thus a certain group of 
organisms is classified by the botanists as belonging to plant- 
life, under the name Myxomycetes, and by the zoologists as 
belonging to animal-life, under the name Mycetozoa, and among 
primitive organisms many are grouped in this two-fold way. 
Yet such classifications are perfectly legitimate, for they cer- 
tainly help in understanding the phenomena under study, 



314 CLASSIFICATION 

and these certainly have connections with plant-life on the 
one hand and animal life on the other. Any method of 
classification, or any group of methods,* is valid, so far as it 
brings us into objective contact with the phenomena under 
study, in such a way as to help on the advance of science. 

Function of Classification in Exposition. — In scientific 
exposition, classification and division exercise two main func- 
tions. In the first place, classification has the preliminary 
function of collecting and arranging the material as a prep- 
aration for proof. The importance of this function can hardly 
be over-estimated. It is only so far as the material has 
been well organised in this preliminary way that we can 
be sure, e. g., that our proof has dealt with all the points 
which stand out as important, and also that it has covered the 
whole ground. That is to say, the objectivity and complete- 
ness of an exposition depend largely upon the efficiency of 
the preliminary classification. Incidentally a good classifica- 
tion adds to the clearness of our exposition. When we can 
see that a subject properly has three main divisions, each 
of which has two sub-divisions, etc., that of itself assists us 
in seeing our way through the subject. The first function of 
classification, then, is the preliminary work of so organising 
the material for exposition that we can proceed to a proof 
which shall plainly be objective and shall patently cover the 
whole ground. 

In the second place, classification and division are, as we 
have seen, a form of organisation which is of a certain general 
type. When we classify, we place individuals in a class which 
is itself part of an organised system, and the individuals 
receive a considerable increment of meaning from being 
placed in such a class. For instance, man as a bare individual, 
apart from his place in society, is a poor thing. Alexander 
Selkirk was monarch of all he surveyed, but he surveyed 
little which was of importance to him as a man, unless he 
gave it a distinctly social reference. Place the individual in 
the class "member of a family," and his significance at once 
increases proportionately. As a husband and father he is 
more of a man than when monarch of a desert island, and 
if we place him in the class "citizen" — i. e., in the class of 
men who think for themselves on political questions, and vote 

i E. g., Bosanquet's application of botanical categories to logic. This 
' 'transgression into another kind" was deliberately practised by Royce 
in seminar-work with advanced students. 



VALIDITY OF CLASSIFICATION 315 

as they think right, his significance increases still more. He 
takes his place in the forward march of humanity. When 
further we place him in relation to science, art, and religion, 
we begin to realise something of his full stature, and to form 
a more adequate idea of man's place in nature. That is to 
say, this second function of classification consists in remedy- 
ing, to some extent, the one-sidedness and arbitrariness of 
many of our preliminary classifications. Final classification 
endeavors to take a large view of the subject in all its more 
fundamental relations. In this way it leads gradually to 
placing the subject in its full setting, in its proper place 
in the system of scientific knowledge. 

Summary. — Classification is thus a kind of organisation 
which assists in the advance of science. In exposition it 
gives us clearness, objectivity, and completeness, especially 
when we are dealing with mind-made entities, but also to a 
considerable extent when we are dealing with the world of 
natural phenomena. Its typical forms are valid so far as they 
lead to genuine insight, and classification as such on the 
one hand prepares the way for proof, and on the other leads 
logically to the construction of a system of the departmental 
sciences. 

FOR FURTHER READING 

H. Ix>tze, Logic, pp. 120-142. Chr. Sigwart, Logic, Vol. II, pp. 158- 
168. W. Wundt, Logik, (3rd Edit.), Vol. II, pp. 47-64. 

EXERCISES 

1. In how many ways might the following be usefully classified : 
Man, month, mountain, river, wind, nation, island, country, tree, 
state, city, girl, book, frog, bulrush, rhododendron, life, consciousness, 
Robinson Crusoe, Mt. Blanc, Ruskin, October, America, oak, Minne- 
apolis, death, plant x 2 , dinner, penknife, prayer, New York, Mary, 
animal ? 

2. Is there any viewpoint from which the following classifications 
are strictly legitimate : (a) Clothiers, land-ladies, book-sellers, (b) 
Children, barking dogs, automobiles. (c) A candid friend, and a 
deadly enemy, (d) A lama (as defined in the exercises to the pre- 
ceding chapter) and an unsuccessful literary man. (e) Poetry, paint- 
ing, music, dancing, (f) Corn-stalks, wood shavings, and old news- 
papers ? 



CHAPTER XXIX 
PROOF 

Proof is considered such an important part of logic, that 
certain logicians have defined logic as the science of infer- 
ence and proof, and in the ordinary consciousness there still 
lingers on, the medieval conception of the logician as the 
trained reasoner "who makes the schools ring with his sic 
probo" In modern logic, however, it is discovery which is 
regarded as the chief function of trained thought, and proof 
is relegated to a very secondary position. It is still regarded 
as important, and part of the training of every scientist con- 
sists of proving some thesis, usually in connection with the 
attainment of an academic degree. In exposition it is vital, 
and almost all the methods used in definition and classifica- 
tion are employed as preliminary to the real work of exposi- 
tion — proving one's thesis. 

Nature of Proof. — We prove hy first constructing a hypo- 
thetical mental model and then testing it to see whether it is 
correct, i. e., whether it actually applies in detail to the situa- 
tion in which we are interested. In certain cases the mental 
model is a re-construction rather than a construction. Thus, 
given a long addition sum, we construct a mental model by 
adding from below upwards, from the bottom of each column 
to the top, in the ordinary way. But in order to prove 
whether our answer is correct or not, we re-construct the 
situation by adding again. We may add in precisely the same 
way as before, or we . may start at the top of each, column 
and proceed downwards. Another form of reconstruction in 
frequent use is to divide the whole column up into tens, and 
add up each ten lines separately, then each ten of those ten, 
and so on, until the whole is added. The second addition, or 
the addition in some other direction, is a way of guarding 
against misleading associations, and assuring ourselves that 
we have really counted all the figures and have omitted or 
misread nothing. 

Let us examine another example. Let us prove that 

316 



NATURE OF PROOF 317 

AB=BA. We begin by constructing a mental model. Let 
. . . .—A, and let —B. Then =1 row of B. 



[ =2 rows of B } and — a rows of B. 



We now proceed to 'prove that A rows of B = B rows of A. 
If we turn the mental model which we have constructed, upon 
its side, we see that the top row makes 1 row of A, that the 
two top rows make 2 rows of A, and that the whole figure 
makes B rows of A. That is to say, our mental model is at 
one and the same time, (1) A rows of B, and (2) B rows 
of A, and we can realise this by counting vertically and 
horizontally. We then, by a reconstruction in which we use 
crosses or other symbols in place of the dots, come to realise 
that the symbols used, and also the actual number of the 
symbols, make no difference to the truth of the model — so 
that A X B = B X A generally. Q. E. D. 

The whole point of the proof in this case consists simply 
in our apprehending what we have done in our construction. 
We find that in constructing A rows of B, we were at the 
same time inevitably constructing B rows of A. That is, we 
find that AB and BA are two aspects of a single construction. 
It is a case of reason apprehending what it has itself put into 
the figure, and becoming perfectly conscious of the implica- 
tions of its own procedure. This example may be regarded as 
representative of all algebraical proofs of the kind we use in 
solving problems by means of equations — let x = this and 
y = that, etc. — and indeed as representative of all mathemat- 
ical proofs generally.! 

Let us take a non-mathematical case. In order to prove 
whether black is or is not a positive sensation, we first con- 
struct the appropriate situation, and then observe whatever 
is to be observed. The "construction" here consists in enter- 
ing the laboratory dark room and closing the door. The con- 
ditions being experimentally controlled, we may be certain 
that no ray of light will enter to stimulate the eye, and that 
accordingly here, if anywhere, the sensation of black is to be 
experienced. The "proof" consists simply in observing closely 
our visual sensations, from the first confused blur of after- 

1 The student is advised to look up a few of the Euclidean proofs, 
with their three stages. (1) statement of the problem, (2) construc- 
tion of an appropriate situation, and (3) "proof," or insight into the 
relations involved in the constructed figure, in order to verify this 
statement. 



318 PROOF 

images which we find on first entering the room, to — what- 
ever ultimately results. When we reach this ultimate state 
of the visual organs — say in thirty or forty minutes — we per- 
form the experiment over again, and persuade other persons 
to join us. We also try various other kinds of construction — 
such as looking at a piece of "Hering black" paper, at a piece 
of black velvet, etc. If the results agree, we regard our 
answer to the problem as proved, much as in the case of the 
addition sum considered above. The stringency of the proof 
depends largely upon the appropriateness of the situation and 
the strictness with which the conditions are experimentally 
controlled. Thus the velvet is better than the paper, and the 
dark room is better than either, and here also, the whole point 
of the proof seems to consist in our apprehending what we 
have ourselves brought about by means of the "construction. " 

Aim of Proof (A) Objectivity. — The aim of proof in logic 
is always, in the first place, objectivity. It is from the 
structure of the phenomenon under study that we try to 
prove that things must be so and not otherwise. A mental 
model which was not a model of the phenomenon under 
consideration would be so far irrelevant, and worthless as 
evidence. We proceed by constructing the phenomenon itself, 
or at least a mental model which is as objective as may be, 
in order to see our way into the case actually before us. 
In proving his thesis, a scientist always endeavors so to 
arrange and marshal the objective evidence as to make it 
plain to his colleagues that he has kept in closest touch 
with the objective facts throughout, and that his construc- 
tion is of objective significance. Anything else would be 
recognised as being beside the point, and thus, from a logical 
point of view, entirely worthless.2 

(B) Completeness. — In the second place, proof aims at 
completeness. If there are five vital elements in the situ- 
ation, it will not do to prove only two or even three. It is 
necessary to prove all five. For example, if we wish to 
prove that Mr. X's dog bit the president's dog so that the 
president's dog died, it is necessary to prove (1) that one 
dog did actually bite another, (2) that the dog which did 
the biting was Mr. X's dog, and (3) that the dog which was 
bitten was the president's dog, and (4) that the bitten dog 
died, and (5) died in consequence of the bite. In a case of 

2 Cf . the case of A 7 -rays, referred to above (p. 192). 



AIM OF PROOF 319 

this kind which the writer has in mind, (3) and (5) were 
never proved, though there was "strong presumptive evi- 
dence." In actual fact, however, the president's dog was 
not bitten, and is still alive. 

Our construction of the mental model must include all the 
relevant features. Thus, in the attempted "proof" that the 
universe is equal in size to a lump of sugar, because each is 
divisible to infinity, and infinities are equal — it is forgotten 
that division in no way increases or diminishes the size of 
the object divided, so that if the sizes were strikingly dif- 
ferent before division, they will remain strikingly different 
after division, however much infinities may be numeric ally 
equal. The omission would be at once observed if it had been 
urged that each object could be divided into two halves or 
four quarters, and that two halves = two halves, or four 
quarters = four quarters, etc. But once the word "infinity" 
is used, the vital omission seems to escape our attention. 
Our mental model, then, must be not only objective, but also 
complete. 

How Far Realisable? (A) With Mind-Made Entities. — How 
far can this aim be realised? Let us consider first the case 
of mind-made structures. Mathematical examples have been 
given above, and mathematical proof is sometimes taken as 
a type of what demonstration should be, strict, rigorous, 
exact. We proceed by constructing a mental model, com- 
posed of dots, lines, or other quantitative or spatial symbols, 
and seem by these means to obtain an insight into the inter- 
relation of the parts of our mental model — an insight which 
is usually satisfactory in point of both objectivity and com- 
pleteness. In the world of mathematical entities, where our 
mental model and the subject we are studying coincide, there 
can be no doubt of the objective reference of our pro- 
cedure. We construct the object itself, and in so doing come 
to realise its various implications, in a way which we find 
adequate, though not, perhaps, incapable of improvement. 

In respect of completeness, however, a certain doubt may 
be felt. It is well known that the proofs of many of the 
theorems in Bk. Ill of Euclid emplo}' the full definition of 
the circle, in cases where a knowledge of conic sections 
shows that something less than the full definition of the 
circle would have been sufficient. That is to say, certain of 
these proof-models are too complete, in that they use too 



320 PROOF 

much argument and evidence, including certain elements 
which, strictly taken, are irrelevant. Further, the existence 
of "alternative" proofs raises a certain doubt. Are such 
proofs equally objective, and equally complete? Compare, 
e. g., the modern proof of Euclid 1. 13 with the original proof. 
The modern proof takes a straight line ABC, and points out 




A B J 

that the angle ABC = two right angles. By taking *> straight 
line BD, pivoting on B, and moving from a position coinciding 
with BA to a position coinciding with BC, it is easily realised 
that the space ABC remains equal to two right angles, how- 
ever it may be divided up by the successive positions of BD. 
This is far more direct than the Euclidean proof, which makes 
use of the addition of equals to equals, etc., and does not give 
so much insight into the spatial relation involved as is given 
in the modern proof. The proof which is more direct appears 
to be more objective and more complete. 

Let us take another example. How do we prove that "The 
supply of game for London is steadily going up . . ." 
means "The game is up . . ."? We prove it by con- 
structing the plan of the cipher — every third word — and then 
reading off the first, fourth, seventh, etc., words, and finding 
that these make sense, and a sense which is strictly appro- 
priate to the whole situation. The proof consists in con- 
structing a mental model which really gives insight into the 
relations involved, and is in fact the model in accordance 
with which the cipher was originally constructed. The clinch- 
ing element about the proof is that it works. Its details 
coincide with the details of the example, just as in Euclid's 
superposition method the triangle ABC coincides with the 
triangle DEF, and it makes sense, i. e., perfectly fits the cir- 
circumstances. Such a proof is both objective and complete, for 
the mental model exactly coincides with the object in ques- 
tion. In geometry, however, where we are studying the nature 
of space, and this is not entirely mind-made even though 
we move in an almost closed circle of definitions, postulates, 
and axioms, — i. e., mental models — our proof was not so 



AIM OF PROOF 321 

wholly objective and complete. In dealing, then, with mind- 
made entities, we can say that, so far as they are truly 
mind-made, our proofs can be both objective and complete, 
but that so far as they are not fully mind-made, but deal 
with such an entity as the nature of space, they are not fully 
objective and not fully complete, but admit of scientific prog- 
ress in both these directions. 

(B) With Natural Phenomena. — In dealing with objects 
other than mind-made entities, we use, as we have already 
seen, mental models for most of our intellectual operations. 
Proof is no exception is this general rule, and proof moves 
wholly within the realm of mental models, especially of a 
mathematical type. We realise this especially in the case of 
physical science. Such proofs deal with objects only in 
respect of their mathematical properties — i. e., only so far as 
they coincide with ideal units, ideally straight lines, etc. 
Thus we prove that if a ladder slides down a wall, the path 
described by someone who is in the middle of the ladder will 
be the arc of a circle. But this is strictly true only if we 
suppose the ladder to be fairly represented by a mathe- 
matically straight line, the side of the house and the surface 
of the ground by a mathematically exact right angle, and the 
person in question to be occupying the mathematical center 
of the ladder. It is well known that a certain allowance has 
to be made, in practise, for some divergence from the exacti- 
tude of the mathematical model, and that such proofs are 
thus not entirely objective and not entirely complete. 

Let us take another example. In laboratory psychology 
there is an experiment with free associations which bears 
upon criminology. A student commits one of two artificial 
"crimes/' the conditions of which are established beforehand 
by the experimenter. The experimenter does not know which 
of the two he has committed, but proceeds to test him by 
calling for associations in connection with a list of stimulus- 
words, some of which bear upon crime A, and some on crime 
B. The reaction-time for each association is taken, and if 
the reaction-time for associations connected with crime A is 
noticeably longer, on the average, than the reaction-time for 
associations connected with crime B, the student is pro- 
nounced guilty of crime A. The proof consists in construct- 
ing the two possible association-situations, and seeing which 
gives the longer reaction-time. There is an. average reaction- 



322 PROOF 

time for every individual, and a noticeable departure from 
that reaction-time must have a special reason. For laboratory 
purposes, such a proof is regarded as sufficient.3 

In actual laboratory practise, this mental model works 
fairly well, and in medical practise Psycho-analysts use it 
as a regular method of investigation. But it is neither per- 
fectly objective nor perfectly complete. There are nearly 
always lengthened reaction-times on the side of the crime 
which has not been committed — though these are not, as a 
rule, numerous — and the reactions to words of criminal import 
are not always lengthy, but may be within the limits of 
probable error. There is thus room for improvement in 
the technique of the method, and in general we may say that 
wherever, as in the case of such natural phenomena, there is 
a gap between the mental model which we employ and the 
facts which we are attempting to study by its means, our 
proof falls short, precisely to that extent and for that reason, 
of objectivity and completeness. 

Validity of Proof. — In the ordinary use of terminology, an 
argument or mental model must be valid, before it is digni- 
fied by the name of "proof." If it is not valid, if it falls 
short of proof, it is given some other name, such as "pre- 
sumptive evidence." We shall accept this terminology, and 
shall refuse to regard as proofs, mental models which are 
invalid. All proofs, then, as such are valid. But, as we 
have seen, there are degrees of validity. The history of a 
science such as mathematics sufficiently shows that a number 
of alternative proofs of a conclusion are equally possible, 
but that some of them enter more directly into the nature 
of the relations studied — i. e., are, as we have seen, more 
objective and more complete than others. Validity is thus 
seen to be a matter of objectivity and completeness, and the 
degree to which a proof is valid can thus be judged ade- 
quately only in the light of further progress in scientific 
knowledge. Evidence may be sufficient to prove our point 
without exhausting the possibilities of proof. For example, 
circumstantial evidence is often sufficient to prove a man 
guilty in the courts. But few authorities would regard cir- 
cumstantial evidence as the most satisfactory form of proof. 

3 The method is sketched very briefly. For further information, 
consult A. A. Brill, Psychoanalysis, Ernest Jones, Psychoanalysis, and 
the papers by Jung and Freud in the American Journal of Psychology 
for 1910. 



TYPES OF PROOF 323 

It is a little indirect and external, and evidence of this kind, 
which looked like overwhelming proof, has occasionally been 
overthrown by evidence of a more direct character. Proof, 
then, is valid so far as it gives genuine insight into the 
relations in question, i. e., so far as our mental model coin- 
cides in its main outlines with the structure of the object 
with which we are dealing. Except in the case of purely 
mind-made entities such as ciphers, it is never final, but is 
progressive, and the degree of its validity can only be judged 
in the light of further scientific advance. 

Types of Proof. — The most frequent model used for pur- 
poses of proof is undoubtedly the mathematical type of 
model. In physical science the importance of such a type 
of proof has long been recognised as supreme, and since 
the days of Plato the mathematical model has been regarded 
as constituting almost the ideal kind of proof. But taken 
strictly, there are at least as many possible types of proof 
as there are possible subjects of exposition, and for some 
of these the mathematical type of proof would be regarded 
as merely preliminary, while for others it would be wholly 
inadequate. For example, in ethical and religious questions, 
a mathematical type of proof may well be used in marshaling 
evidence and arranging one's data, but such a method is 
merely preliminary.^ It is of assistance in preparing the 
ground, but in dealing with an ethical question, what we 
desire is an insight which is ethical. So too in dealing with 
historical questions, or questions of musical technique, math- 
ematical types of proof can at best play only a very sub- 
ordinate part. On the whole, then, there are so many types 
of model which can be regarded as possible, that it is 
unprofitable to attempt to enumerate and classify them. 

It is usual, however, to distinguish two typical forms of 
proof which differ, not in respect of the kind of model used, 
but rather in the way in which this is applied and in the 
kind of insight to which it leads. These are known as (1) 
direct proof and (2) indirect proof. All the instances pre- 
viously studied in the chapter would be considered cases 
of direct proof. Direct proof attempts to construct such a 
mental model of the situation with which we are dealing, 

4 For the scientific application of mathematical models to religious 
questions, consult the Journal of Religious Psychology, and on ethical 
questions, the International Journal of Ethics. 



324 PROOF 

that it shall be possible to attain to a simple, straight- 
forward, and direct insight into the relations involved, as 
when we superimpose one triangle directly upon another, or 
when we reconstruct a situation which is in question, by 
appealing to the evidence of trust-worthy eye-witnesses. 
Indirect proof is like the reductio ad absurdum in Euclid. 
It attempts to prove that A must be B on the ground that 
the contradictory supposition leads to absurdities. 

Let us consider an example of indirect proof. To prove 
that A did not personally murder B, in spite of his known 
motive to do so, and in spite of circumstantial evidence 
against him, it is enough to prove that A was in another 
town at the exact time when the murder was committed. The 
alibi is a convincing form of indirect proof. We construct 
a mental model of the situation, and find that it cannot pos- 
sibly be made to square with the supposition of A's personal 
guilt. That is to say, from direct insight into the require- 
ments of the situation we see that another suggested mental 
model will not fit. Into this incompatibility also we have an 
insight which is direct. An indirect proof of any statement 
thus consists of a direct refutation of the contradictory oppo- 
site. Hence it has been suggested by Herbert Spencer that 
a criterion of truth is the inconceivability of the opposite, 
and in practise there is no doubt that indirect proofs may 
be of great assistance in bolstering up an attempt at direct 
proof which is not perfectly convincing. But what is con- 
vincing about the so-called "indirect" proof, is not its indi- 
rectness, but its direct side. We believe that A could not 
possibly have personally murdered B, because we have direct 
proof that he was in another town, and because we can see 
directly that it was necessary for him to have been at the 
scene of the murder if he is to be regarded as guilty of the 
charge. We compare these two mental models, and see 
directly that they are incompatible. The nature of proof, 
then, is fundamentally to be direct, and so far as it falls 
short of directness, so far it falls short of convincing us of 
its validity. Logically, then, proof is always direct. 

Summary. — We prove by constructing a mental model of 
the situation in question, in such a way as to make clear 
the inter-relation of elements in the model which we have 
constructed. Reflection upon our own construction leads to 
an insight which is direct and convincing. The aim of such 



VALIDITY OF PROOF 325 

mental models is objectivity and completeness, and in cases 
where our construction gives us the object itself, this aim 
can be attained. In the case of natural phenomena, however, 
where there is a gap between the mental model and the 
phenomenon in question, we can only approximate to com- 
plete objectivity. While it is usual to distinguish an ''indirect" 
form of proof, the nature of proof is essentially direct, and 
the degree of its validity can be determined only in the 
light of further advance in knowledge. As knowledge is 
never complete, but progressive, so proof is never absolutely 
final, but advances with advancing science. 

FOR FURTHER READING 

H. Lotze, Logic, Bk. II, chapter iv. Chr. Sigwart, Logic, Vol. II, 
pp. 192-210. W. Wundt, LogiTc, (3rd Edit.), Vol. II, pp. 65-85. 

EXERCISES 

How could you prove : (a) That you really are where you think 
you are. (b) That Napoleon ever lived, (c) That 459 — 387 = 72. 
(d) That a bird in the hand is worth two in the bush, (e) That a 
university degree is a desirable asset, (f) That Beethoven was one 
of the greatest musicians who lived within the last two hundred 
years. (g) That lying and stealing are wrong. (h) That life is 
worth living, (i) That corn will not grow if planted early in the 
spring? 



CHAPTER XXX 
FALLACIES 

Fallacies are older than logic. Indeed, one of the chief 
motives which first led to logical study was the reaction from 
sophistry or the deliberate use of fallacies to deceive and 
entangle others. In consequence of this interconnection 
between the search after truth and the avoidance of falsity, 
some study of the nature of fallacy has always formed an 
integral part of scientific method. No one entirely escapes 
falling into these errors. Even logicians of the caliber of 
John Stuart Mill have made mistakes in this way which others 
have pointed out, but which they themselves were never 
able to see. At the present day, fallacious agruments are not 
so frequently used with deliberate intent to deceive as was 
perhaps the case in ancient Athens, and it is more a question 
of putting ourselves upon our guard, so as not to fall into 
these traps which await each one of us, and so deceive our- 
selves. 

Definition of Fallacy. — Fallacies are sometimes defined as 
failures to prove — i. e., as though it is in relation to attempts 
at proof that they are especially noticeable. It is certainly 
true that a fallacy proves nothing, and that if the aim of 
the thinker who fell into the fallacy was to prove something, 
he has failed of his aim. But this definition is not wide 
enough for scientific accuracy. Many a fallacy into which we 
frequently fall can hardly be brought under the head of proof. 
For instance, there may be failures to judge or to infer 
correctly, failures in analysis and synthesis, in abstraction 
and determination, failures in induction and deduction. And 
though all of these may indeed be used as methods of proof, 
they are far more frequently used as methods of investi- 
gation. It is thus possible to fall into fallacies in respect 
of investigation, as well as in exposition. So too in exposition 
there are fallacious attempts at definition and classification, 
as well as at proof. There is no limit to the opportunities 
for error, and they are quite certainly not restricted to the 

326 



OCCASIONS OF FALLACY 327 

field of attempted proof. We shall therefore define fallacies 
as mistakes in thinking — using the term thinking in its widest 
possible sense. 

Occasions of Fallacy. — The pursuit of truth takes place, as 
we have seen, by the construction of mental models. Falla- 
cies arise when these mental models are used in some way 
which is incorrect. There are three main possibilities of such 
incorrect use: — (1) in relation to the data which furnish our 
starting-point — the mental model which we construct may 
misrepresent the concrete situation which we are attempting 
to understand, as when the paranoiac interprets the most 
innocent actions of the persons around him as the deliberate 
designs of conspirators. (2) In the second place, there may 
be no mistake about the data as such, or about their relation 
to the mental model, but the model itself may contain some 
logical flaw, such as an inconsistency. This is frequently the 
case with our typical rules in ethics and esthetics. Unless 
formed with the utmost care, these rules often contain certain 
inconsistencies which only become apparent in the course of 
time, as their consequences develop and lead, perhaps, to 
results the opposite of what we had intended. i (3) In the 
third place, the application of our mental model to concrete 
facts may be careless and so lead to mistakes, as when we 
attempt to apply any system of theoretical principles in 
practise, or to carry out general orders in detail. The appli- 
cation of any general principle is full of dangers of this type. 

Fallacies of this general kind may arise either in investi- 
gation or in exposition. In exposition, however, there is an 
additional occasion of error. This arises from the fact that 
in exposition there are at least two parties, the writer or 
speaker on the one hand, and the reader or hearer on the 
other. There is thus a certain duality of outlook which leads, 
perhaps inevitably, to certain mistakes in understanding. The 
speaker has his set of mental models, and the hearer has his. 
These two sets are bound to be partly different, in view of 
the differences in education and in habit of mind. The hearer 
translates what he hears, into his own set of mental models, 
and in so doing can hardly escape a large number of errors. 
We see this most clearly, perhaps, in the case of foreigners. 

i For a number of instances of rules taken even from physical 
science, cf. F. H. Bradley, Appearance and Reality, the first half of 
the book. 



328 FALLACIES 

When we hear an address in French or German, we translate 
it into our own ideas or mental models, and there is, as we 
all know, much which cannot possibly be translated with 
absolute correctness. And if, perhaps, we do not understand 
French or German correctly, and the foreigner in question 
can not understand us correctly either, our attempts at con- 
versation are pitiable indeed. 

Such fallacies arise from a difference of mental model. 
What A means in one sense, B may translate into an entirely 
different set of mental models. This can take place in a 
single language just as well as in two, as will be seen if 
we consider one or two instances. 

Where do you live, Pat? With Mike. 

Where does Mike live? With me. 

But where do you and Pat both live? Sure, isn't it together 
that I'm telling you we live? 

The difficulty arises here from perfectly honest misunder- 
standing. The mental model of the questioner is spatial. He 
wishes to know Pat's street address, whereas Pat's mental 
model is social, and has not the remotest glimmering of a 
connection with spatial questions. Such mistakes are ex- 
tremely common in every walk of life, as well as in scientific 
exposition. We may, perhaps, notice one more example. 

She: Do you admire me for my intellect, or for my beauty? 

He: Not for your intellect. 

She: .Flatterer! 

In this case She assumes as an explanation of their situa- 
tion the mental model of admirer and admired, while He 
assumes the mental model of borer and bored. In this case 
the divergence of mental models is very thinly disguised, and 
may well be deliberate on both sides, as is so frequently the 
case on occasions which call for the employment of social 
"tact." 

Such cases of a confusion of two logically distinct mental 
models may even happen to a single individual. The best 
known instance is Mill's famous fallacy: — 

The only proof that an object is visible is that 
people actually see it. The only proof that a sound 
is audible is that people actually hear it. And so of 
the other sources of our experience. In like manner, 
the sole evidence that anything is desirable, is that 
people actually desire it. People do actually desire 



OCCASIONS OF FALLACY 329 

Pleasure. Therefore, Pleasure is desirable, or Good, 
and in fact the Chief Good. 

The argument proves that pleasure is something which 
people can desire, but Mill takes it as proving that it is a 
"good" or something which they ought to desire. The con- 
fusion is thus between a psychological and an ethical mental 
model. Such mistakes are very common in attempts to prove 
ethical, esthetical, or religious beliefs in terms of models 
which are psychological, economic, or biological — i. e., other 
than ethical, esthetical, or religious.2 

Yet another occasion of fallacious thinking arises from 
the way in which the written or spoken language may suffer 
from slips in the mechanism of expression, so that one model 
is intended, but another suggested. This is extremely 
common. E. g., from a New York paper: 

WANTED. A groom to look after two horses of a 
pious turn of mind. 

A second-hand morris chair for a bach- 
elor with richly carved claw-feet. 

In every-day cases like these, we can usually distinguish 
what was intended from what is suggested. But any student 
who has done much translation from one language into 
another will know that there are many ambiguities, arising 
probably from some slip in the mechanism of expression, 
where no ingenuity can succeed in discovering what the 
original author may have meant. This is particularly well 
known in the case of the Greek and Latin classics, where a 
most elaborate technique has been developed for dealing 
with just such errors. In many cases, however, the text 
proves to be hopelessly corrupt, and the modern editor resorts 
to emendations of his own — i. e., reconstructs the passage in 
accordance with a mental model which appears to him to 
satisfy the requirements of the situation. The fallaciousness 
of such emendations, however, is universally admitted. 

From these considerations, we realise that the occasions of 
fallacies are to be sought in the relation of our mental 
models to the facts of experience. Our constructions may 
differ from the facts with which we start, or from the facts 
to which we wish to apply them, or from other possible 
models based upon the same data. 

2 Cf. Locke's "proof" that it is impossible to be a sincere Atheist, 
in the Essay, Bk. IV, chapter x. 



330 FALLACIES 

Characteristics of Fallacy (A) Subjectivity. — However fal- 
lacies may arise, there are, however, certain characteristics 
which they one and all exhibit. In the first place, fallacy is 
subjective. All thought and all reasoning, whether for pur- 
poses of investigation or for purposes of exposition, ostensibly 
aims at truth — at bringing us into connection with objective 
facts and objective laws. It is because a thought somehow 
fails of establishing this connection that it is called a fallacy. 
We are left on the hither side of the fence, and take our 
own ideas, our mental models, for the realities.3 At times, 
we even take the symbolic expression, the word itself, for the 
reality, and try to substitute for insight into the reality a 
futile discussion based upon the philological characteristics 
of the word. Thus a student, asked in an examination in 
formal logic to define the technical term "contrapositive," — 
which is one of the forms of "immediate inference" — answered 
that it was something which was (1) not positive, for it 
was opposed to the positive (contra in Latin means "against"), 
but also (2) not entirely negative. For example, "counter- 
feit money" was opposed to the positive, for it was false 
currency, but was also not entirely negative, for you could, 
perhaps, succeed in passing it! 

As a general rule, then, we fall into fallacies, when this 
takes place, by getting lost in the mechanism of our own 
thinking, whether this is due to the complication of our 
mental models, or arises from substituting the word for the 
thing. The mental model comes between us and the reality, 
and our thought remains satisfied with a superficial inter- 
pretation, which seems good to us, at least for the time 
being, but will not withstand a serious comparison with the 
objective facts. Thus the hasty classical student translates 
the famous line Frigidus in pratis cantando rumpitur anguis 
as "The cold meadow-snake bursts into song," (instead of 
"is torn asunder by magic charms"), or. . . . et odora 
canum vis as "and a powerful smell of dogs," (instead of "and 
a keen-scented pack of hounds"), — and is thoroughly satisfied 
with his entirely original rendering. So too many novelists 
are satisfied that they are thoroughly in touch with real life, 
when as a matter of fact they are revelling in a world of 
mental models which are mental fictions. Subjectivity, then, 

3 Cf., in this connection, the first few pages of Plato's Republic, 
Bk. VII. 



SCOPE OF FALLACIES 331 

or failure to get into touch with objective facts, is one of the 
chief characteristics of fallacious thought. 

(B) Incompleteness. — A second characteristic of fallacious 
thinking, is its incompleteness. We leap at conclusions which 
are false, only because we do not pay sufficient attention to 
the evidence before us. If we always adhered to careful 
methods of analysis and synthesis, mistakes would more 
rarely arise. But we pass over something without noticing 
it, and the consequences of such a slip, slight perhaps in 
itself, may be serious. Thus, to suppose that the country is 
prosperous because many business men are making money, 
and all our acquaintances happen to be doing well, is a 
mistake which arises from incomplete observation. Other 
cases are not so serious. When the Home Guard Private 
asked, "If we join the National Guards, what will be our 
relations with the other units,"? it was sufficiently obvious 
that he meant, would his battalion — the parent organisation 
— be numbered 1 or 13. It was perhaps deliberate incom- 
pleteness of observation which made the Major (who didn't 
know) answer, "Friendly — at least I hope so." So too with 
the child's reasoning, "A penny is a copper (coin), and a 
"copper" is a policeman, and a policeman is an officer (of 
the law), and an officer (of the naval or military forces) is 
a gentleman; therefore a penny is a gentleman." Each step 
in continuing such an argument can be taken only by one 
who is wilfully blind to many elements in each transition. 
Incompleteness, then, is a second characteristic of fallacious 
thinking. 

Scope of Fallacies. — There is no limit to the scope of fal- 
lacious thought. In the sphere of mind-made entities, mis- 
takes creep in almost as readily as when we are dealing with 
natural phenomena. By a slight mis-drawing of the figure, 
which passed unobserved, it has seemed possible to demon- 
strate that one right angle is equal to, and greater than, 
another right angle, or that parallel straight lines meet 
before reaching infinity. So too in ethical, esthetical, and 
religious thought, the confusion of mind in which we so 
easily involve ourselves is too well known to require illus- 
tration. So also in attempting to solve unfamiliar problems, 
in mathematical as well as in every-day thinking, we often 
use the method of trial-an&error. We go astray a few times 
before striking into the right path. Still, in the end, we 



332 FALLACIES 

can escape error almost completely in this field. But in the 
case of natural phenomena, complete objectivity, as we have 
seen, appears to be out of our power. Successive generations 
can approximate to a more accurate comprehension of the 
workings of nature, but a full comprehension is denied us. 
We use models which never quite fit the concrete circum- 
stances, and our empirical interpretations are thus neces- 
sarily infected with error. To some slight extent our best 
and finest efforts at understanding the world in which we 
live are mistaken; and there is only one way of avoiding 
fallacy in this field — viz., by preserving a slightly sceptical 
attitude of mind towards all claims of finality. To recognise 
the trap is to avoid falling into it, and while our thought 
in this field is necessarily imperfect, it is not necessarily 
fallacious. It would be fallacious only if we thought we 
knew in cases where we have only presumptive evidence. 
There is no fallacy, so long as we maintain the Socratic 
attitude, and at least know that we don't know. At the same 
time, we should transcend the Socratic position in believing 
that the broad basis of experience, upon which our modern 
science rests, enables us to approximate to a knowledge 
which for practical purposes is becoming progressively more 
adequate. 

Source of Fallacy. — From the viewpoint of pure logic, there 
is no such thing as error. When we think logically, we think 
truly, and it is only so far as we fail to follow the rules of 
pure logic that we deviate into fallacies. A purely rational 
being never errs. True, perhaps, — but then, do we know any 
purely rational beings? Living, as we do, in a world which 
we experience through senses which are easily confused and 
deceived, and with a memory which we trust, in spite of its 
known treachery, only because we have nothing better in 
which to trust, and with powers of self-deception which frame, 
as valid and logical, reasonings which are mere distorted 
reflections of instinctive wants, or of social conventions which 
have long since lost what little semblance of reason they 
may once have possessed — is it any wonder that we fall, 
time and again, into the same old fallacies, as well as con- 
stantly blundering into new ones? 

We have a dual nature. On the one hand, we have the 
demands of a logical reason, voiced in the ideal conceptions 
of truth, goodness, beauty, and the like. On the other hand 



TYPES OF FALLACY 333 

we have the mechanism of our nervous system, with its 
sense-organs at one end and its muscles at the other, an 
instrument devised for practise rather than theory, cradled 
in instinct and educated in custom, and inherently incapable 
of satisfying the ideal demands of pure reason. If with such 
an instrument we believe we can fulfil the demands of tran- 
scendent thought, we fall necessarily into fallacy. The only 
escape from this ever-present source of error is to recognise, 
once and for all, that perfect satisfaction of these ideal 
demands is out of the question for beings whose sole mech- 
anism for fulfilling such demands is a central nervous system 
developed through the dark ages of animal evolution. 

The utmost we can do is so to organise our experience as 
to approximate to making sense of it — to bring our ideals 
into connection with the facts, and to elevate the brute facts 
in the light of our ideals, as far as this may be possible, 
and thus create a science and a mode of life which shall 
combine actual experience and ideal desire, and gradually 
and progressively approach the haven where we fain would 
be. If we fully recognise this, the chief source of fallacy 
will be removed. If we know, not only what we want, but 
also what we can get, we are not likely to confuse the two. 
And if, avoiding that confusion, we go to work to create 
that science and that life which are possible for us, sub- 
stituting breadth of experience where depth of insight seems 
denied us, we shall realise the fruits of the Socratic spirit, 
and shall act out the highest life which is in our power — a 
life self-determined, free, and raised above the deeper sources 
of self-deception. 

Types of Fallacy. — There are no special types of fallacy. 
All fallacies partake of a single form — viz., confusing mental 
models with the more concrete realities of experience, — and all 
attempts at enumerating and classifying typical forms of fal- 
lacious thought either (1) re-state the general nature of fal- 
lacy, or (2) mention some special occasion of possible error. 
But these are too many to be enumerated. For example, the 
best known type of fallacy is what is called Petitio Principii, 
or begging the question. It is usually illustrated by such 
examples as circular definition, or as the explanation of some 
event in terms of itself. E. g., "A cause is that which pro- 
duces an effect, and an effect is that which is produced by a 
cause," "Wood is the ligneous part of trees," "The poppy (in 



334 FALLACIES 

medicine) sends people to sleep, quia est in eo virtus dormi- 
tiva" "We are able to remember what has happened to us 
because we possess the faculty of Memory," etc. A minor type 
of such false assumption is known as the "fallacy of double 
question" — e. g., "Have you decided to settle down to a decent 
kind of life at last?", "What have you done to your coat?" A 
second well known type of fallacy is called Ignoratio Elenchi 
or irrelevant proof. This is illustrated by brow-beating a wit- 
ness, attacking the personal character of an opponent, or rais- 
ing some national issue, instead of arguing on the facts of 
the case, and generally by appealing to prejudice, hope, and 
fear, rather than to reason. But it is easy to see that every 
instance of false assumption is also an instance of irrelevant 
proof, and that every instance of irrelevant proof is an instance 
of false assumption. In fact, we have here, not two typical 
forms of fallacy, but two statements of the essential nature 
of all fallacious thought. To think that an assumption of 
ours amounts to proof is to confuse a mental model with the 
reality, and to appeal to emotion or prejudice rather than to 
reason, is to attempt to substitute a subjective mental model 
for an objective understanding of the facts. Such attempts 
are clearly re-statements of the essential nature of fallacy as 
such. 

So too the celebrated division of fallacies into two classes, 
(1) in dictione, and (2) extra dictionem — i. e., fallacies in 
language rather than in thought, and fallacies in thought 
rather than in language, respectively — breaks down in the 
face of serious criticism. In the first place, the distinction is 
thoroughly artificial — for as thought expresses itself in lan- 
guage, and language is a mere vehicle or mental model for 
expressing thought, all mistakes in language are due to mis- 
takes of thinking. Thus the typical "fallacy of accent" — e. g., 
"Saddle me the ass. And they saddled him" — could not pos- 
sibly arise unless there were some inattention of thought and 
thus some failure to grasp the meaning. So too in the comic 
opera, when Patience, who "cannot tell what love may be," 
mentions that she once had a beloved playmate, "and, by the 
way, he was a little ~boy" the Chorus immediately reply that 
they "thought as much — he was a little ~boy." Patience rejoins, 
"Remember, pray, he was a little boy." The variations of 
accent follow the variations of meaning, and it is impossible 
to separate the words from the thought. In the second place, 



TYPES OF FALLACY 335 

if we admit that linguistic usage is at times misleading, as in 
the famous oracle, "Pyrrhus, I say, the Romans can subdue," 
such ambiguities of accidence or syntax are but single occa- 
sions of error, and are as nothing when compared with the 
vast and unclassified field of such occasions. If we wish to 
avoid a fallacious and superficial clearness, we shall refuse 
to attempt a classification of these special occasions of error, 
and shall assert that all fallacies belong to a single type — viz., 
the confusion of mental models with realities or with other 
mental models. 

FOR FURTHER READING 

W. R. Boyce Gibson, The Problem of Logic, chapter xxxiii. H. 
Plato, Euthydemus. Lotze, Logic, Bk. II, chapter vi. J. G. Hibben, 
Logic, Part II, chapter xvi. 

EXERCISES 

Are the following arguments fallacious, and, if' so, in what does 
the fallacy consist: (1) "Who rules o'er" freemen should himself be 
free"? You might as well say, Who drives fat oxen should himself 
be fat ! (2) It is a mistake to say that the best judges in matters 
of art are always in a minority. For, consider — suppose it true that 
the minority are always the best judges, and carry it to extremes. 
The smallest minority consists of one man. If the principle is true, 
then each man will himself be the best judge, and there will be as 
many best judges as there are individuals who differ from others, and 
thus constitute extreme minorities. But this is absurd. Therefore, 
the majority are always the best judges. (3) Let x = a, then ax 
= a2, and ax — x2 = a2 — x2 i. e., x(a — x) = (a + x) (a — x), and 
by cancelling, x = a + x, i. e., x = 2x, or 1 =: 2. (4) I am a Chian, 
and no Chian can open his lips without telling a lie. Therefore I 
lied when I said I was a Chian, etc., so that I am not a Chian — in 
which case, perhaps, I told the truth, and thus am a liar after all. 
(5) Other people cannot be as sensitive as I am; for they do not 
make the same fuss about their feelings as I do. (6) Mr. X is a 
sound man for Senator, for he made an excellent after-dinner speech 
the other evening. (7) I could be a great artist, if it were not for 
my environment; for I feel it within me. (8) Mr. Z is not to be 
trusted as mayor for his table manners leave much to be desired. 



CHAPTER XXXI 
THE SYSTEM OF THE SCIENCES 

In periods of scientific development, a tendency arises in the 
direction of applying scientific method in somewhat narrow 
channels, and perhaps — in view of the vast body of scientific 
knowledge and the exacting requirements of modern technique* 
— such specialisation is inevitable. Inevitable or not, how- 
ever, it is certainly the tendency, and the modern student, 
after years of study, sometimes complains of bewilderment. 
He cannot see the wood for the trees, and feels a need for 
breadth, as well as depth, of vision. He wishes to form a 
mental picture of experience as a whole, and not only of what 
he sees through his microscope or in his test-tube. In answer 
to this dissatisfaction and vaguely formulated demand, there 
have arisen attempts to systematise the results and principles 
of the various departmental sciences, and thus to give a single 
world-picture which shall be just to all the chief discoveries 
of science, and shall at the same time satisfy the craving of 
the mind for unity and totality. The best known examples 
of such attempts are found in the "Synthetic Philosophy" of 
Herbert Spencer, and — to a lesser extent — in the more exact 
but not less unwieldly tomes of Wilhelm Wundt. On a minor 
scale, however, most modern writers on logic attempt to draw 
together the various lines of inquiry and envisage them as a 
whole. 

Nature of Such Systematisation. — Such systematisation is, 
in the first place, a last and most gigantic attempt at analysis 
and synthesis. We wish to take all knowledge for our prov- 
ince and put it together. That is synthesis. We wish also to 
put it together in a way so articulate and organised that we 
can see the inter-relation of the parts in the light of the whole. 
That is (partly) analysis. We wish our system to be both 
analytic and synthetic. 

i This is true not only of laboratory sciences like physics and 
chemistry, but also of the social and linguistic sciences. History and 
philology have their technique as well as microscopy and histology. 

336 



AIM OF SUCH SYSTEMATISATION 337 

In the second place, such systems are both abstract and 
determinate. They are abstract. It is impossible for one 
man to carry in his head at one and the same time all the 
detail of science, and consequently the world-picture which we 
desiderate, will have to be largely in outline. That is to say, 
it will necessarily be abstract. Medieval metaphysics, which 
largely follows the conception of Aristotle,2 is highly abstract. 
According to this conception, we pass from the more concrete 
and detailed knowledge to the higher or "first" principles, 
simply by leaving out the detail and retaining the bare out- 
line. The highest and intellectually most abstract of all is 
the concept of Being, and the chief function of a system of 
first principles is, from this viewpoint, to study the nature of 
Being qua Being — apart from its specific differentiations in 
the wealth of detail which we find in nature. A man, month, 
mountain, nation, wind, all are, or have Being. But they have 
different kinds of Being. The kind of Being which a month 
has is very different from the kind of Being which a man has, 
or even which a mountain has. The science of ontology, how- 
ever, was intended to abstract from all these differences, and 
deal with the concept of bare Being. It is easy to see that 
the final world-picture in terms of pure Being, would turn 
out to be the barest of bare skeletons, with all the life and 
color gone. 

In more modern times, however, and especially since the 
work of Hegel, thinkers have tended to regard the picture of 
the whole as more determinate and concrete, and to view the 
isolated fragments of the system — particular elements of expe- 
rience — as thin and poor in content, in short as abstract. For 
the modern viewpoint, a concept is not abstract qua intel- 
lectual, and concrete qua sensory, but is abstract qua fragmen- 
tary, and concrete as seen in its place in a totality. For this 
view the concept of Being is not the poorest and most empty 
of content, but the richest and fullest of all contents. It con- 
tains within itself the principle of determination of all the 
specific forms of Being, and instead of being an abstract skele- 
ton, made up of only the single element common to all entities, 
is the richest of all beings, containing as it does the infinite 
variety of nature, and all possible, as well as all actual, details. 
It is produced by addition rather than by substraction, and is 

2 Aristotle's view is developed in the Metaphysics. Cf . in particular, 
Met. I, i. 



338 THE SYSTEM OF THE SCIENCES 

the sum-total of Reality, the Absolute or ens realissimum.3 
It is thus the most concrete and determinate of concepts, 
though it is still regarded as partly abstract.* 

In the third place, such a system is the final work of induc- 
tion and deduction. It is to be the final mental model of the 
universe, and should sum up in itself all the preceding labor 
of analysis and synthesis, abstraction and determination, by 
proceeding to determine, as far as possible, the law of the 
Whole. It is usual to regard this law as the law of Reason, a 
principle of organisation, by means of which the whole uni- 
verse is regarded as a vast individual, containing within itself 
both identity and difference. 5 

Finally, it is possible also to regard such a system as a sin- 
gle gigantic definition or as a final classification, and this 
view has exercised considerable influence upon the work of 
Spencer and Wundt. Such attempts at classification have been 
very numerous, and we shall consider some of the best known 
types later. In general, then, we can say that the nature of 
such systematisation is to complete, at least in general out- 
line, the work of investigation and exposition, to round it off 
in some way, so that the specialist, at work upon his partic- 
ular portion of the whole, may also form a mental picture of 
the whole, and may thus realise his unity and fellowship with 
his co-workers in other parts of the field. 

Aim of Such Systematisation (A) Objectivity. — The aim 
of such systematisation is not, however, merely to frame a 
single model of the whole, so that the specialist may not feel 
lost or cut off from his fellows. We aim at something more 
than a cure for intellectual Heimweh. In actual fact, almost 
everyone frames some sort of idea of experience as a whole, 
of the meaning and value of life, and of the place of man in 
the universe — i. e., reacts in some way to what have been 
called the Great Problems. These reactions, however, tend to 
be somewhat arbitrary and subjective, and reflect a somewhat 
narrow and eclectic viewpoint. Optimism and pessimism, for 
instance, are ordinarily somewhat shallow, and have little 
hold upon objective facts. They are usually prejudices, rather 
than scientifically tested models, and the aim of scientific 

3 Cf. G. Simmel, Hauptprooleme der Philosophic chapter 1, F. H. 
Bradley, Appearance and Reality, Part II. 

4 Cf. H. Joachim, The Nature of Truth, last chapter. 

5 Cf. F. H. Bradley, Principles of Logic, pp. 449-450. 



AIM OF SUCH SYSTEMATISATION 339 

exposition in systematising, precisely as in denning or classi- 
fying, is, before everything else, to be objective.^ 

It is not merely to satisfy our craving for unity and totality 
of outlook, that we systematise. For that craving can be sat- 
isfied by almost any sort of mental model. Every religion, 
every code of thought current in artistic, commercial, charit- 
able, and family circles, has its own solution of this problem, 
and such solutions are found fairly satisfactory, so far as the 
needs of such circles go. But the scientifically minded man 
wants something more than the mere satisfaction of a sub- 
jective desire — he wants to know the facts. He wishes his 
'system to be satisfactory, not merely to himself, in a sub- 
jective way, as a kind of registering of his private and unstand- 
ardised reaction to the universe as he happens to experience 
it. He wishes his system to be objectively valid, and to be 
true of experience as a whole. For instance, many people 
regard the whole universe as revolving around themselves or 
the interests of their immediate friends or profession. This is 
a narrow and prejudiced view, and the aim of scientific expo- 
sition is at something more all-inclusive, and more definitely 
in contact with objective facts and objective laws. The first 
aim, then, of such attempted systematisation, is objectivity. 

(B) Completeness. — In the second place we aim, here if 
anywhere, at completeness. A partial or one-sided view is here 
wholly out of place. Aut totum, aut nihil. The materialistic 
view of the universe, for instance, is one-sided and incomplete. 
Viewing all reality as matter in motion, and all science as 
specialised effort to solve special problems of moving matter, 
it tends to leave out all the characteristic work of the mental 
and moral sciences, and is of very little use as a working 
hypothesis in the historical and philological sciences. It is 
incomplete, and thus, as a view of the whole, is a travesty of 
the facts.? So too the study of truth-values, such as we have 
in logic and in the natural sciences, is one-sided, unless atten- 
tion is paid also to the. ethical, esthetical, and religious valu- 
ings, and a purely theoretical view of the whole is unjust to 
three-fourths of life — just as perhaps a purely practical view 
of the whole, or a view purely esthetical, is equally incom- 

6 Cf. A. O. Lovejoy's presidential address to the American Philo- 
sophical Association, Philosophical Review, Vol. XXVI, 1917, pp. 123- 
163. 

i For a clear exposition of materialism, see Buchner, Matter and 



340 THE SYSTEM OF THE SCIENCES 

plete.8 In attempting to set up a mental model which shall 
represent the universe as a whole, it is necessary to be at 
least as complete as is possible, and to leave unrepresented no 
class of experiences, no view of the facts, however distorted. 
The idea of the whole must be aZZ-embracing — i. e., must be 
complete. 

How Far Realisable? — How far can we put together the 
various lines of scientific effort, and systematise them so as to 
present a world-picture which shall be both objective and com- 
plete? It is not difficult to see that this cannot be wholly 
accomplished. In the first place, our sciences are not wholly 
objective. They consist of mental models which do not per- 
fectly correspond to the facts, but are in a process of trans- 
formation which renders them ever more and more acceptable 
from an objective point of view. Where complete objectivity 
is not to be found in the data to be synthesised, complete 
objectivity can hardly be expected in the total picture. In 
the second place, no single science is anything but incom- 
plete, and it is not held that the subjects of scientific inquiry 
will ever be completely understood. Here also we have only 
approximation towards our goal, and here also we must admit 
that if the data are incomplete, the whole which is to be con- 
structed out of such data must itself be at least equally incom- 
plete. A synthesis of our various lines of scientific inquiry, 
then, cannot be wholly objective and cannot be wholly com- 
plete, in the sense of giving us a final world-picture. This 
has become so well known, that at the present day the idea of 
constructing such a world-picture has been abandoned, and in 
its place it is proposed merely to attempt to put together our 
mental models and instruments of investigation in a way which 
shall be just to them — i. e., to relate the sciences, imperfect as 
they are, to one another, and to discover, if possible, the 
relation of historical inquiry to philosophical or to palaeonto- 
logical research, or the relation of histology to botany and 
zoology, or the relation of psychology to the whole field of 
scientific inquiry, etc. In a word, the aim is no longer to 
present a final picture of the world as it is — for no one man 
and no group of men has the requisite knowledge— but rather 
to systematise the sciences as we have them at the present 
day, and thus to understand the interrelation of our own 

8 Of. Varisco, The Great Problems, pp. 26-27, 286 ff., Appendix V. 



TYPES OF SUCH SYSTEMATISATION 341 

methods and mental models. As this inquiry is definitely and 
explicitly confined to the world of mind-made entities, we can 
approach it with more confidence. In principle, at any rate, 
it should be capable of realisation. 

Types of Such Systematisation. — In the history of science, 
there have been many attempts at such systematisation, at 
embracing the work of science as a whole and viewing it from 
a single standpoint. One of the most famous is the system of 
Plato. He has (1) a general view of the whole field of human 
knowledge, and (2) a special view of the field of scientific 
inquiry. The general view is known as the "four stages of 
intelligence," and is symbolised in the accompanying diagram. 
In the lowest stage of intelligence, we have the attitude of 
uncritical acceptance of any and every view, devoid of the 
faintest vestiges of scientific method. In the second stage we 
have the attitude of practical common-sense, which tests the- 
ories only in the light of their immediately practical work- 
ings. In the third stage we have what we should call the field 
of the departmental sciences. Things which we can touch and 
see are here dealt with only so far as they throw light upon 
laws in some department of scientific inquiry, and the interest 
in this field is an interest in law, rather than in things or 
opinions. In the fourth and final stage, an attempt is made 
to transcend the limitations of the departmental sciences and 
construct an undepartmentalised view of reality as a whole, 
by the use of pure reason. This is the field of metaphysics. 

So much for the general view of human knowledge. The 
third stage, which contains the field of science, is divided up 
in accordance with the principle of passing from the simple 
to the complex, and turning the soul from the changeable to 
the permanent and eternal. First we have arithmetic, then 
plane geometry, solid geometry, astronomy, and harmony, and 
finally a study of the mutual association and relationship of 
these sciences, which teaches us the ties which bind them 
together— what we might, perhaps, call epistemology. This 
bridges the way to the science of sciences, dialectic, which 
corresponds, in a rough and approximate way, to what we 
have recognised as the field of transcendent judgments.9 

The number of sciences thus recognised by Plato is extremely 
small — "imperfect" and empirical sciences are expressly 

9 Cf. Plato's Republic, from the last few pages of Bk. VI to half 
way through Bk. VII. 



342 



THE SYSTEM OF THE SCIENCES 



Fourth Stage 

Dialectic or Metaphysics 



Third Stage 

Science 



Second Stage 

Common Sense 



Lowest Stage 



Epistemology (?) 
Harmony 
Astronomy 
Solid Geometry 
Plane Geometry 
Arithmetic 



excluded from his scheme — and all belong to a single group, 
the mathematical group, which leads on to epistemology and 
metaphysics. The philological, social, and historical sciences 
find no place in the scheme,io and the sciences which he does 
admit, are admitted only on the ground that they are busied 
with the eternal rather than with the empirical, and are thus 
adapted to turn the eye of the soul away from the world of 
sense-perception, and to develop our powers of "pure" rea- 
soning. 

This view has been, and still is, extremely important in its 
influence upon religious minds, and upon the minds of those 
who are especially interested in the ideal development of 

10 Plato does, perhaps, recognise political science, but this represents 
the practical application of dialectic, and hardly finds a place in the 
third stage of intelligence. 



VALIDITY OF SUCH SYSTEMATISATION 343 

humanity. But from the point of view of the scientist who 
wishes to be just to all lines of scientific inquiry, it is clearly 
unsatisfactory. It is neither objective nor complete, and the 
reason for its failure to solve our problem is to be sought in 
the fact that the viewpoint, from which the different lines of 
inquiry are united, is external, and belongs to a theory of the 
ideal nature of man, rather than to scientific research itself. 

As representative of more modern attempts to solve this 
problem, it will be, perhaps, sufficient to consider the scheme 
of Wundt. As will be seen from the acc6mpanying diagram, it 
attempts to be both objective and complete, and to give a 
mental picture of the interrelation of all lines of actual scien- 
tific inquiry. 

Validity of Such Systematisation. — Complete validity in 
such attempts at systematisation is hardly to be looked for. 
The nature of the attempt to systematise is largely descrip- 
tive. And to describe accurately and completely the relation 
of the various sciences to one another is hardly possible. The 
reason for this is to be sought in the fact that there are, at 
the present day, no final or hard and fast lines of distinction. 
The botanist has to be something of a chemist and mathema- 
tician. He frequently has to know something of geography, 
geology, and zoology, something of the general theory of evolu- 
tion, and sometimes even of psychology and logic. So too the 
psychologist requires knowledge of biology, of physics, and of 
sociology, as well as of mathematics. Every specialist uses, 
in actual practise, whatever he finds necessary to the solution 
of his special problem, regardless of its place in the "system," 
just as the comparative anatomist pays little or no attention 
to the system which we find in zoology. Where the work of 
scientists thus cuts across any lines which the systematiser 
may draw, it is plain that description of the work of science 
can hardly be expressed in any of the typical systematic 
forms, if we wish to be objective in our description. Complete 
validity, then, is out of the question. 

What the systematiser can aim at, however, is a reasonable 
completeness, and at some principle of organisation which 
makes his system convenient for purposes of reference. Such 
a system as Wundt's certainly fulfils this aim, and is so far 
to be regarded as valid. But it remains sufficiently obvious 
that any such system must be arbitrary and from many view- 
points unsatisfactory; and if we keep in mind the concrete 






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SUMMARY 345 

needs of scientific research and scientific exposition, we shall 
see that no one system can possibly be regarded as final, even 
for purposes of reference. For example: for certain purposes 
a group of Medical Sciences is advisable, and for certain other 
purposes a group of Social Sciences. Yet neither of these 
demands receives satisfaction from such a system as that of 
Wundt. All that we can hope for, then, in this field, is a 
system which shall present us with a general view of the work 
Qf science, in a way which is fairly accurate and reasonably 
complete. Complete validity, however, even in the case of 
this purpose, is not to be expected. 

Summary. — So far we have seen that, in answer to cer- 
tain needs arising in an age of over-specialisation, attempts 
are made so to systematise the special sciences as to present 
us with a general world-picture. This attempt is eventually 
given up as unscientific at the present stage of knowledge, and 
in its place we try to arrange the lines of actual scientific 
inquiry in such a way as to obtain a general view of the work 
of science. This too is found to be unsatisfactory in point of 
objectivity and completeness, and the only purpose which it 
can reasonably be expected to serve is, convenience for refer- 
ence. This aim also cannot be completely accomplished, but 
systems such as that of Wundt are at least helpful and sug- 
gestive. 

FOR FURTHER READING 

J. G. Hibben, Logic, Part II, chapter xvii. Herbert Spencer, Classi- 
fication of the Sciences. W. Wundt, Logik, (3rd Edit.), Vol. II, pp 
85-100. 



CHAPTER XXXII 
THEORY OP SCIENTIPIG METHOD 

The Problem. — So far we have discussed in detail the 
chief characteristics of scientific method, whether for pur- 
poses of investigation, or for purposes of exposition. It now 
remains to put together what we have discovered, and to 
formulate a general theory of scientific method, comparable 
to the theory of judgment and the theory of inference dis- 
cussed above. The general nature of scientific method plainly 
consists in framing some mental model or hypothesis in ref- 
erence to a given situation, and then attempting to under- 
stand the situation in terms of the mental model, or of some 
modification of that model introduced after further reference 
to the given situation. All that we really understand or are 
able to take into our mental grasp is, in the last analysis, the 
structure of the mental model itself; but we can make this 
progressively more adequate by continued reference to the con- 
crete situation. This "reference" takes place by means of 
sense-perception. There are thus two factors in the use of 
scientific method, (1) the sensory, by which we are able to 
keep in some sort of touch with the natural environment, and 
(2) the intellectual, by means of which we construct and 
modify our mental models. To frame a "theory" of scientific 
method, it will be necessary to treat each of these factors sep- 
arately, before taking them together, and to treat them in two 
ways. In the first place we shall state what part they actually 
do play, and by this description answer the question of fact. 
In the second place we shall examine briefly the objectivity 
and completeness of the results so attained, and by this criti- 
cism answer the question of validity. 

The Sensory Element in Scientific Method. (A) Mind- 
Made Entities. — In the case of mind-made entities, sense- 
perception plays a very minor role, but still a role which is 
both appreciable and necessary. In experimenting with a 
jig-saw puzzle or a cipher, the sense of sight plays an appre- 
ciable part, and the sense of touch may also come into play. 

346 



THE INTELLECTUAL ELEMENT 347 

In solving mathematical or ethical problems, many sensuous 
elements appear to be indispensable, though they are, of course^ 
in no sense final. Elements other than sensory play the chief 
part, but here also, as in the case of natural phenomena, sen- 
suous perception is a condition without which we could have 
no scientific knowledge, and its function is, to keep us in 
touch with the concrete situation, whatever that may be. 

(B) Natural Phenomena. — In dealing with natural phe- 
nomena, it is only by means of sense-perception that we become 
aware of them. It is only by means of our senses, sight, hear- 
ing,' and the rest, that the physical world is given to us in the 
form of concrete situations. We build houses out of materials 
which we can touch, see, and handle. The earth on which we 
live, the rain and sun, the changing seasons — even our books, 
music, and art — all these are given to us, in the first place, 
by way of sensuous perception. And yet, sensation plays no 
final part. The world of physical science is very different 
from the sensations of color, sound, and contact, with which 
our sense-organs respond to stimulation. Sensation is only 
one element in scientific method, and its function is to furnish 
us with a starting-point, a concrete situation which we can 
proceed to analyse and synthesise, etc., until our intellectual 
aspirations are satisfied, so far as this is possible. 

The Intellectual Element. (A) Mind-Made Entities. — In 
scientific method, the part played by intellectual elements is 
far more in evidence. The whole matter of constructing mental 
models, and deducing consequences from the general plan of 
such models, is a matter for the intellect. The way in which 
these models are constructed, however, has perhaps not been 
made sufficiently clear. They are constructed, in every case, 
by applying the intellectual standards of identity, difference, 
and organisation, internal and external, so far as such appli- 
cation proves to be possible. The case of analysis and syn- 
thesis has been dealt with, at least in principle, in an earlier 
chapter.! In the case of abstraction, it is still more obvious 
that in singling out for special attention some one element or 
aspect of the situation which results from analysis, we are 
applying the standard of identity, and that in excluding from 
consideration every element or aspect other than the one espe- 

i Chapter xvi, where analysis and synthesis are dealt with, in prin- 
ciple, under the heading of "analytical expansion" and "systematic 
constructiveness," respectively. 



348 THEORY OF SCIENTIFIC METHOD 

cially selected, we are applying also the standard of differ- 
ence. So also in the case of determination. We determine a 
single element or aspect by placing it experimentally in a 
number of contexts, each of which is different, and each of 
which adds a new determination to the single element with 
which we started. In this case, it is sufficiently obvious that 
the standards of identity, difference, and organisation are 
being used. Finally, in the case of induction and deduction — 
elaborate methods which use every resource of the preceding 
methods in establishing some law — it should be sufficiently 
plain that the same standards are being used, though in a way 
which is more complex, as the situation and the methods 
employed are, as a general rule, more complicated. So too 
definition usually involves some kind of statement of what 
the object defined is, and some distinction of it from objects 
which are like it but are regarded as different; and classifi- 
cation is very definitely an organisation or system which con- 
tains a number of differentiated elements, each of which may 
be regarded as an identity. So too proof proceeds by construct- 
ing a mental model which represents the situation to be 
proved. This, like all mental models, is a little system built 
up out of elements which are mental counters, differentiated 
identities, and the same standards govern our constructions in 
the case of proof as in the previously mentioned cases. 

(B) Natural Phenomena. — With natural phenomena we 
deal, as we have already seen, indirectly. We construct mental 
models in the form of hypotheses, and by trying out one of 
these after another come as close to understanding the nature 
of such phenomena as we can. In constructing these mental 
models we use the same intellectual standards of identity, 
difference, and organisation, to which we have already referred 
in the case of mind-made entities, and in general, the part 
played by intellectual elements, considered by themselves, is 
approximately the same in the two cases. It is, in fact, only 
in relation to sensory elements that a difference can be estab- 
lished. This difference consists in the fact that problems con- 
cerned solely with mind-made entities can as a rule be com- 
pletely solved, while problems concerned with natural phe- 
nomena cannot be completely solved. That is to say, our 
mental model may be the mind-made entity itself — the object 
studied, and the model in terms of which we approach the 
study of it may completely coincide. But in the case of nat- 



THE INTELLECTUAL ELEMENT 349 

ural phenomena, such coincidence is an ideal towards which 
we can progressively approximate — but some gap always 
remains. So far, then, as the construction of mental models 
as such is concerned, there is no difference between the two 
cases. In dealing with natural phenomena, as in dealing with 
mind-made entities, we construct our experimental models in 
terms of the intellectual standards of identity, difference, and 
organisation. 

"Summary. — Thus we see that, so far as the description 
of scientific procedure is concerned, the theory of scientific 
method resembles the theory of judgment and the theory of 
inference. Sense-perception furnishes us with the starting- 
point for our intellectual operations, and the intellectual oper- 
ations consist in taking to pieces and rearranging the material 
given in the concrete situation, in such a way that we obtain 
insight into its laws and principles. This taking to pieces 
and rearranging takes place by the experimental construction 
of mental models which we then proceed to test and verify by 
reference to the datum. Compared with judgment, the field 
of scientific method corresponds approximately to the field of 
symbolic judgment, and the typical example of both is the 
algebraical solution of some concrete problem by means of 
simultaneous equations. In symbolic judgment, however, the 
field seems perhaps a little wider, while the mental models or 
symbols of which science makes use seem more restricted to 
quantitative and causal models. The difference is, however, 
only apparent. For though science does make use chiefly of 
these two types of sj'mbol for interpreting our experience, it 
can and does use other models also, and in principle is pre- 
cisely as unrestricted as is symbolic judgment. 2 

Compared with inference, again, there is but little difference. 
Both proceed by analysis and synthesis, by taking apart the 
given situation and reconstructing it in the light of intel- 
lectual standards, and both use approximately the same meth- 
ods and the same standards. But the field of inference is per- 
haps slightly wider than the field of scientific method, for it 

2 Scientific method in practise is restricted to the field of theoretical 
values, and takes no account of ethical, esthetical and religious values 
as such — i. e.. qua ethical, esthetical. and religious. This is because 
these values do not lend themselves to explanation in terms of either 
mathematical or causal models. But in principle they may some day 
be a part of science. 



350 THEORY OF SCIENTIFIC METHOD 

covers the ground of judgments of experience also,s and even 
— to some slight extent — the ground of transcendent judg- 
ments. Scientific method, however, is rigidly restricted to the 
symbolic reconstruction of its data, and sharply distinguishes 
itself from any attempt to transcend the field of possible expe- 
rience. It is thus a specialised and concentrated application 
of inference to a somewhat narrow part of the whole possible 
field. 

Validity of Scientific Method. (A) Mind-Made Entities. 
— In the light of our previous chapters, we can state briefly 
the conditions of the validity of scientific method. As we have 
seen, it is possible for scientists to make mistakes. Analysis 
and synthesis, abstraction and determination, induction and 
deduction, of themselves are not infallible; and as we pointed 
out in the chapter on Fallacies, it is possible to go astray even 
in dealing with mind-made entities. Owing to accidents of 
educational environment, different people tend to use slightly 
differing sets of mental models, and it is hard for A to under- 
stand exactly the mental models of B. There is thus in all 
exposition a certain amount of marginal error, which can, of 
course, by careful attention be reduced to a minimum. But 
when all is said and done, some slight difference between the 
symbolic tools or models used by A and the mental instruments 
used by B tends, in practise, to remain, and is thus a constant 
source of error. But the chief source of error is undoubtedly 
to be sought in the relation of the intellectual to the sensory 
element. As we saw in the case of the symbolic judgment, 
even in dealing with text-book problems — which are certainly 
mind-made entities — it is very easy, in the preliminary analy- 
sis and synthesis which gives us the x and y equations, to 
omit or add something which, slight though it may be in itself, 
yet vitiates in some degree all subsequent inferences and con- 
clusions. So also in the verification, when we come back from 
our deductions and compare these detailed consequences of our 
mental model with the details of the concrete situation, it is 
very easy to overlook a few obstinate facts in favor of a fas- 



3 Scientific method also contains generalisations from experience, 
arrived at by abstraction and determination, and thus to a slight 
extent, enters the field of experiential judgment also. But its chief 
work lies more in the field of symbolic judgment. 



VALIDITY OF SCIENTIFIC METHOD 351 

cinating theory.* This is especially likely to happen where 
the original situation is complex. These occasions of error 
are always with us, and invalidate a large percentage of our 
attempts to apply scientific method. 

Still, in dealing with mind-made entities, there is no doubt 
that we can be entirely successful. Our procedure can be both 
objective and complete. The conditions of its validity are sim- 
ple, and are the same as the conditions already noticed as 
indispensable for validity in judgment and in inference. The 
sensory apprehension must be direct, and the intellectual con- 
struction must obey the intellectual norms of identity, differ- 
ence, and organisation, and finally, the sensory and intellectual 
elements must be brought together correctly. That this can be 
accomplished, our success in solving mathematical problems, 
in solving ciphers, and — in many cases — in solving ethical, 
esthetical, and even religious problems, sufficiently attests. In 
dealing with entities which are strictly mind-made, complete 
validity is possible. 

(B) Natural Phenomena. — In dealing with natural phe- 
nomena, we have already seen that complete and final validity 
is out of the question. It is, however, possible that our meth* 
ods — e. g., the mathematical treatment of physical, psycho- 
logical, and even sociological problems — may be valid as far 
as they go. On what does their validity depend? It depends 
upon the same conditions as we discovered in discussing judg- 
ment and inference. So far as the sensory apprehension is 
direct, it is ultimate and must be accepted. So far as the 
mental models are framed strictly in accordance with intel- 
lectual standards, they also are ultimate, and must be accepted. 
Finally, so far as both sense and intellect are correctly brought 
to bear upon one and the same problem, it can so far be solved, 
and solved in a way which is valid — though perhaps it remains 
incomplete. The only adequate test of validity in these cases, 
where our sensuous apprehension is not perfectly direct, and 
our intellectual efforts seem confined to the indirect trial-and- 
error method which tests one mental model after another 
until it approximates to discovering something which will 
"work"— in such cases the only adequate test of validity is the 



4 One of the best known instances in recent years is the late Dr. 
Verrall's interpretation of the Agamemnon of Aeschylus. Substan- 
tially all the critics are agreed that it is "brilliant, but not convinc- 
ing." The Baconian view of Shakespeare is another famous instance. 



352 THEORY OF SCIENTIFIC METHOD 

advance of science itself. If our methods not only provide us 
with a fair solution of their special problem, but are also 
found fruitful in other fields, and of assistance in helping on 
the advance of scence, they may be looked upon as valid. 

Conclusion. — If we look back over the whole course of 
our inquiries, we find that the endeavor of man to solve his 
problems by the use of logical thought, rather than by trust- 
ing to instinct and feeling, is of a very definite and pronounced 
character. In judgment, we take apart the given, sensory flow 
of experience, split it up into elements which are cut off and 
fixed by the mind, and form differentiated identities out of 
which we proceed to build up an intellectualised model of the 
situation with which we are dealing. In inference, we analyse 
and expand, constructing out of precisely similar intellectual- 
ised elements whole edifices of thought which extend the intel- 
lectually reliable aspects of our experience almost without 
limit. Finally, in scientific method, we reduce this framing 
of mental models to a system, to the methodical application 
of certain tested and approved types of mental model, espe- 
cially of a mathematical character, in a way which leads to 
the gradual but sure advance of scientific knowledge. That is 
to say, the character of logical thought consists in substituting, 
for the vague continuity of sensuous feeling, the highly artifi- 
cial but thoroughly determinate and exact mental counters 
known as concepts. 

With sensation and feeling, we cannot rise above the con- 
crete situation. We live these, we experience these, we are 
these. Sensation, feeling, impulse — these are the stuff of 
which life, as we are conscious of living, is made up. These 
are what are half-revealed by introspection, by looking within 
and attempting — vainly, as it seemss — to place our finger upon 
the pulse of consciousness. They are parts of the stream of 
consciousness, and constitute our life. Our life — but not our 
knowledge. We live them, but cannot contemplate and under- 
stand them. They evade our mental grasp, and leave us vainly 
trying to say many things. We grasp at consciousness, and 
are left with — sl psychological theory. We try to apprehend 
the nature of thought, and are left with — a theory of logic. 
The nature of understanding is, as we say, not intuitive but 
discursive. It is indirect, and constructs intellectualised enti- 

5 Cf. W. B. Pillsbury, Fundamentals of Psychology, p. 7. 



CONCLUSION 353 

ties which are always somewhat different from the realities 
which they are supposed to represent. If we try to under- 
stand, we inevitably construct more or less plausible theories, 
and substitute for the reality the mental construction which 
seems to explain it best. What we understand is thus always 
primarily what our intellect has itself introduced into the 
phenomena studied. The structure built up in the sciences is 
a mind-made structure, and is intelligible precisely in so far 
as it is of the nature of intellect. It is of the mind, mental, 
and has, in relation to the phenomena which we experience, 
an application which is only secondary and indirect. 

At the same time, there is no doubt that logical thought is 
successful. One steamer leaving the wharf a day behind a 
slower steamer may seem to have little to do with algebra, 
and the distant smoke on the horizon may seem perhaps to 
have more connection with poetry than with trigonometry. 
And yet, trigonometry and algebra can give us exact infor- 
mation as to the distance of that smoke on the horizon and 
the hour at which we shall pass the slower steamer, and that 
information will be found to work. Without such mental 
models, our steamer and railroad schedules would be impos- 
sible, and the whole series of conventions and symbols upon 
which our modern civilisation rests would vanish into thin 
air. Logical thought works. It is tested and found valid at 
every moment of our every-day life, as well as in the labora- 
tories of scientists. 

How are we to explain this validity? How is it that a mind- 
made model will tell us more about the structure of reality 
than our most intimate psychological experiences? We can 
only hint at an answer to this inevitable problem. We can 
account for the success of our mental models only upon the 
assumption that these represent — at least approximately — the 
intelligible structure of the concrete facts of experience, that 
the phenomena of nature have intelligible laws, that the uni- 
verse is essentially rational or even mind-made, and that its 
rationality is akin to the rationality which we discover in our 
own logical thinking. It is, in fine, only so far as our reason 
is identical in principle with the reason embodied in' concrete 
facts, that the unfolding of our own mental constructions can 
bring us into touch with the nature of the universe. The fur- 
ther study of this problem and of this answer belongs, not 
to logic, but to metaphysics. 



354 THEORY OF SCIENTIFIC METHOD 

FOR FURTHER READING 

B. Bosanquet, Logic, Bk. II, chapter vii. F. H. Bradley, Principles 
of Logic, Bk. Ill, Part II, chapters iii-iv. H. Lotze, Logic, Bk. Ill, 
chapter v. Chr. Sigwart, Logic, Vol. II, pp. 548-557. 



INDEX I 



Aeschylus, 351 n. 
Aristotle, v, 3, 61, 142, 199-200, 
218, 273, 280 n., 283, 296, 337 
Arnold, 122 n. 
Ayer, 142 n. 



Erdman, v, 11 n., 38 n., 104 n., 

108 
Euclid, 287-288, 297, 317 n., 

319-320, 324 
Euripides, 191 



Bacon, 211, 351 n. 
Bain, 280-281 
Bakewell, 89 n. 
Benoit, 142 n. 
Bergson, 187 n. 




Finkelstein, 148 n. 
Fischer, 143 n. 
Freud, 143, 322 n. 
Furneaux, 225 n. 


Binet, 154, 218 






Boissier, 225 n. 




Galton, 202 n. 


Bosanquet, v, 4, 11 n. 


, 35 n, 


Goblot, 176 n., 192 n., 283 n., 


91 n., 99 n., 142, 


215 n., 


298 n. 


216 n., 314 n. 




Goldscheider, 286 n., 287 


Bradley, A. C, 142 n. 




Grant, 142 n. 


Bradley, C. G., 122 n. 




Groos, 81 n. 



Bradley, F. IT., v, 11 n., 90 n., 
99 n, 102, 145, 188 n., 202 n., 
327 n., 338 

Bridges, 218 n. 

Brill, 322 n. 

Biichner, 339 n. 

Caird, 143 n. 
Chadwick, 218 n. 
Coleridge, 302 
Condillac, 102, 103 n., 142, 
Copernicus, 274 
Cousin, 142 n. 
Cox, 204 n. 

Davies, 178 n. 
Descartes, 102 
Dewey, v, 254 n. 



Hart, 144 n., 213 n. 
Hartenstein, 142 n. 
Hegel, 4, 102, 143, 161 n. s 

228 n., 254, 337 
Hibben, 123 n. 
Hobbes, 111 
Hume, v., 149 n. 
Huxley, 235 n., 265, 266 n. 

James, 1 n., 144 n., 278 n., 

286 n. 
Joachim, 338 n. 
Jones, A. L., 85 n., 225 n., 

235 n., 266 n. 
Jones, E., 143 n., 322 n. 
Jung, 322 n. 



355 



356 



INDEX I— Continued 



Kant, v, 3, 37, 91 n., 100 n., 

139, 142, 143, 218, 246, 253 
Keller, 154 

Leibniz, 102, 292 n. 

Locke, v, 103 n., 142-143, 151, 

165, 167, 200 n., 201 n., 

250 n., 329 n. 
Lodge, O. J., 268 n. 
Lodge, R. C, 151 n. 
Lotze, v, 108, 121 n. 
Lovejoy, 292 n., 339 n. 
Lully, 292 n. 

MacDougall, 223 n. 

MacLennan, 10 n. 

Marrett, 191 n. 

Meikeljohn, 91 n., 100 n. 

Mellone, 264 n. 

Menander, 191. 

Mill, v, 103 n., 123 n., 125, 133, 

149, 156, ZUZ, 281, 326, 328- 

329 

Nettleship, 121 n. 
Newton, 264-265, 266 
Nietzsche, 273 

Pestalozzi, 3 

Peterson, 148 n. 

Pilate, 56 

Pillsbury, 87 n., 138 n., 164 n., 

233 n., 299, 352 n. 
Plato, v, 3, 90 n., 101, 102, 

112 n., 151, 166, 167, 178 n., 

180, 228 n„ 273, 274, 275 n., 

323,, 330 n., 341-342 
Plotinus, 89 n. 
Porphyry, 156 n. 
Prince, 163 n. 



Royce, 123 n., 142, 314 n. 
Russell, 145 n., 153 n. 

Schelling, 228 n., 259 
Schuppe, 11 n., 125 n. 
Sellars, 202 n. 
Shakespeare, 143, 189-190, 

351 n. 
Sidgwick, H., 88 n. 
Sigwart, v, 112, 120 n., 125 n., 

128 n. 
Simmel, 338 n. 
Socrates, 109, 110, 112, 140, 

332-333 
Spencer, 206, 227 n., 324, 336, 

338 
Spinoza, 19, 61, 142 
Stout, 174 n., 250 n. 
Swift, 164 

Tacitus, 225 
Taylor, A. E., 81 n. 
Tufts, 254 n. 

Varisco, 161 n., 340 n. 
Vaughan, 178 n. 
Verrall, 351 n. 

Wilson, J. C, 156 n. 
Windelband, 11 n., 142 
Wolff, 216 n., 247, 259 
Wundt, v, 2n., 11 n., 23 n., 

3a,n., 108, 215 n., 283 n., 336, 

338, 343-345 

Yerkes, 218 
Zeno, 274 



Index II 



Abstraction, ch. xxii, 11, 17, 

30, 38, 40, 41, 82, 92, 199- 

200, 255 

— and determination, 260- 
262 
Accent, fallacy of, 334-335 
Affirmation, 110, 111, 113-115 
Algebra of thought, v, 292 
Analogy, 31 
Analysis, chs. xiii, xix, 2, 6, 9, 

24, 40, 55, 68, 71, 92, 121, 

159, 198-199 

— and synthesis, ch. xxi, 220 
Anticipations, 14 
Apprehension, intellectual, 37, 

39, 102 

— sensory, 24-40 passim, 172 
A priori, 153, 166 
Aspiration, 33, 60, 74, 102 
Association, 5, 17-30, 40-41 

passim, 58, 71, 74, 82-83, 86, 

139 
Assumption, 4, 333-334 
Attention, 2, 27, 38, 41, 48, 55- 

58, 102, 141, 171-172, 247 
Attitude, logical, 1-4 

Background of experience, in- 
tellectual, 39 

—sensory, 17, 19-21, 34, 38, 
49, 55, 60 

Behavior, 1, 2, 5, 57 

Biology, 4, 38 

Bodily existence, 17, 19 

Card-index, 44, 311-312 



Categorical, 134-136, 172 
Cause, 80, 128 ff., 215-216, 226- 

227 

— Aristotle's doctrine, 296 
Certainty, 23, 28, 30-31, 45 

—See also Validity 
Chaos, 3, 46-49, 179 
Classification, ch. xxviii, 11, 

41, 179, 202, 205-206 
Clearness, 44-45, 47-49, 52, 76, 

179-180, 188, 314 
Coherence, 65, 68, 76, 79, 92, 

96 
Common sense, 3, 4-5, 135 
Comparison, 11, 40, 41 
Concentration, 49, 295 
Concept, 32, 43, 44, 51-52, 58- 

59, 67, 72, 75, 87, 106, 141, 

205, 250, 352 
Conclusion, 3, 4, 25, 27, 38, 

121, 124, 127 
Consequences, 3, 275 ff. 
Consistency, 6, 37, 39-41, 80, 

92, 96, 99, 274-275, 281 
Construction, chs. xv, xx, 13, 

14, 37, 41, 62-63, 124-125, 181 
Contemplation, 82, 84 
Context, intellectual, 82-89 

passim, 95, 181, 193 
Continuity, intellectual, 94, 

96-99 

— sensory, 25-50 passim, 55, 
57, 63, 68, 76, 170 
Contradiction, 43 
Counters, mental, 40, 42, 44, 

95, 97, 181, 184, 348 



357 



358 



INDEX II— Continued 



Deduction, ch. xxv, 203 
— and induction, ch. xxvi 

Definition, ch. xxvii, 2, 136 n., 
204-205 

Demonstration, ch. xxix, 27 

Dependence, ch. xii, 120, 177 

Desire, 31, 33, 53 

Determination, ch. xxiii, 200 
—and abstraction, 260-262 

Diagnostic classification, 312 

Difference, ch. vi, 38-46 pas- 
sim, 68, 91, 94 

Discourse, subject of, 47-52 
passim 

Discovery, 121 ff., 135, 156, 
159, 173, 174, 180, 198 ff., 
263 ff. 

Distinction, 11, 18, 37, 38, 41, 
55, 57, 63, 68, 76 

Distraction, 58 

Division, 307, 309, 314 

Dogmatism, 135 

Efficiency, 3, 5, 44, 198, 221 
Error, ch. xxx, 24, 28, 43, 

68 n., 270, 350 
Evidence, 28-30, 130 
Evolution, 2, 6, 104, 235 
Expansion, analytic, 120-122 
Experimental judgments, 12- 

15, 18-19, 21, 25-28, etc." 
Experiment, 24, 27, 141, 145, 

166 
Explanation, 172, 204-205 
Exposition, 204-207 

Fact, 23, 29 

Faculty physchoiogy, 250, 334 

Failure to judge, 20, 62, 96, 

98, 109-111, 326 

—to prove, 31, 326 



Faith, 60, 145-146 

Fallacy, ch. xxx 

Falsity, 24, 37, 92 

Feeling, 3, 20, 23-24, 33, 38, 

40, 48, 53, 55, 60-63, 68, 70, 

76, 102, 145, 187, 352 
Fiction, 28, 86 
Focus of consciousness, 27, 28, 

32, 33, 39, 40, 101 
Form and formal, 37, 44, 52, 

88 
Generalisation, 18, 27, 30, 201- 

202, 249-250, 261 
Genetic method, 6 
Given, the, 10, 11, 18, 23, 31, 

37, 143, 191, 237-238 
God, 31, 33, 40, 44, 51, 60, 62, 

74-75, 87-88 
Grammar and logic, 7 n., 47-48 
Ground, logical, 80, 114, 128 ff. 

Happening, 23, 29 n., 53, 68, 

71, 76, 77 
History, 6, 28-29, 49-50, 85, 

105-106 
Human experience, 20, 31, 43, 

51-52, 60, 87-88 
Hypothesis, ch. xii, 109, 166, 

274 

Idea, 2, 19-20, 31, 38, 43, 51, 52, 

60, 111 
Idealism, 101-102, 143 
Identical propositions, 55, 59, 

62 
Identity, ch. v, 31, 37-45, 54- 

59 passim, etc. 
Ignorance, 109-112 
Ignoratio elenchi, 334 
Illusion, 24, 31 
Image, 2, 20, 139 



INDEX II— Continued 



359 



Imagination, 20, 51, 112, 139, 

171 
Impersonal judgments, 10 
Impressions, 37, 40, 49, 50, 

102 
Index-classification, 44, 311- 

312 
Individuality, 65-66, 69, 77, 92, 

219, 338 
Induction, ch. xxiv, 18, 27, 30- 

31, 202-203 

— and deduction, ch. xxvi, 
203 
Inductive leap, 158 
Inference, Part II, 125, 193- 

194 
Infinite, 14, 20, 31, 33, 43, 51, 

88 
Insight, 4, 5, 203, 232, 270, 289 
Instinct, 1-3, 38, 1*45, 333, 352 
Instruments, intellectual, 37, 

212, 350 
Intellect, chs. iv-ix, 177, 182, 

347-349 

—and sense, 101 ff., 182, 184- 
185 

— "pure" intellect, 15, 102 
Intelligence, 2, 17, 31, 34, 57, 

149, 218, 224 
Interest, 2, 38, 49, 55-56 
Interpretation, 21, 24-25, 27-28, 

30, 40, 95, 105 
Intuition, 93, 121, 143-146, 172 

— mathematical intuition, 
176 
Inventory, 310-311 
Investigation, 198 ff., 290-291 
Isolation, 199, 201-202, 249-250 



Judgment, Part I 
—defined, 166-167 
—failure to judge, 20, 62, 

96, 98, 109-111, 326 
—field of, 12-15 
— stages of, 11-15 

Knowable, the, 20, 51 
Knowledge, , 4, 30, 43, 80, 102, 

109-110, 149 

—latent, 154 ff. 

Laws, 30, 128 ff., 153, 250, 263 
—of thought, 4, 6, 37, 39-46, 
52, 91-92 

Logic, aim of, v, 352-353 
— applied, 94 
— and psychology, 5-6 
— and natural science, 80, 

90 
—defined, 5-6, cf. 23, 352-353 
— modern, v 
— study of, 3-5 
— symbolic, v, 292 n. 

Logical attitude, 1-4 

Margin of consciousness, 27- 

28 
Mathematics, 3-4, 80, 90, 94, 

214-215, 225-226 
Memory, 17, 26, 27 
Mental counters, 40, 42, 44, 95, 

97, 181, 184, 348 
Metaphysics, 1, 4, 20, 31, 33, 

43, 44, 88, 99, 106, 145, 337, 

353 
Method, scientific, Part III, 

3-5, 103, 135, 142, 145 
Mind, 5, 102, 218 



360 



INDEX II— Continued 



Models, mental, 93, 182, 212- 

213, 258, 269, 278-279, 293-ff., 

327 ff., 348 ff. 
Mysticism, 14, 88-89 
Natural classification, 312-313, 

cf. 294 
Negation, 54, 57, 63, 108-116 
Nervous system, 38, 333 
Novelty, ch. xiv, 39, 57, 122- 

124 

Objective, 24, 109-112, 209, 

223, 269-270 
Organisation, chs. vii-viii, 40- 

58 passim, 92, 96 

Perception and inference, 124- 

125 
Perceptual judgments, 9-10, 

17-18, 23-25, 38-40, 46-48, etc. 
Perfection, 31, 33, 52, 60, 76, 

88 
Personal experience, 28, 30, 

31, 41, 49, 73 
Personality, 32-33, 43 
Petitio principii, 333-334 
Phenomena, 102, 223, 271, 291 
Plurality of causes, 133-134 
Popular thought, 133, 136, 

283-284 
Practise and theory, 3-5, 135 
Predicate, logical, 47-55 pas- 
sim 
Premises, 121, 124, 127 
Present, the, 26-27, 39, 40, 50 
Problems, human, 1-2, 60, 353 
Proof, ch. xxix, 3, 31, 205, 

206, 314 
Propositions and judgments, 

7n. 
Psychology, 5-6, 88, 109, 144, 

146 



Purpose, 65, 77, 209 

Quality of sensation, 17, 18, 
21, 34, 244 

Rationalisation, 144 
Reality, 2, 33, 44, 99, 102, 253 
Reason, 20, 37 
Reasonableness, 6, 26, 32, 35 
Reconstruction, 19, 28-31, 42, 

73, 191 
Relations, 39, 65-67, 80, 94, 98, 

102, 108 ff., 152 ff., 170, 173- 

174 

Schemata, 142 

Science, 27, 30, 41-46, 58, 80, 

89, 135, 271, 275, 332, 336 ff. 
Selection, 71, 75, 77, 84, 86-87 
Self, 33, 60, 62, 74, 88 

— feelingfl7, 20, 38, 39, 91 n. 
Sensation, chs. ii-iii, 37, 47, 

53-56, 76, 93, 102, 149, 169 ff., 

346-347 

— and judgment, 17 ff. 

—and intellect, 101 ff., 182, 
184-185 

— and validity of, ch. iii 
Sensualism, 102-103 
Simple judgments, 9-10, 15 
Situation, concrete, 141, 146, 

170 ff., 186, 189 ff. 
Standards of truth, 5-6, 37-46, 

52, 91-92 
Statistics, 69, 148, 214 
Subject, logical, 47-55, passim 
Subjective, 20, 109-112 
Symbolic judgment, 12-15, 19- 

21, 31-34, 41-42, 49-50, 58-60, 

etc. 

—logic, v, 292 n. 



INDEX II— Continued 



361 



Synthesis, ch. xx, 200-201 
— and analysis, ch. xxi 

System of judgments, ch. 
xxxi, 39-41, 44, 68, 76, 80- 
81, 86, 89-92, 95-98 
— nervous system, 38, 333 

Tabula rasa, 2, 37-38 
Tests of validity, 23-24, 34, 42 
Theory and practise, 3-5, 135 
Things-in-themselves, 31, 187 
Thought, 2-5, 15, 20, 33, 39, 56, 

58, 73-74, 89, 115, 280, 353 
Totality, 65-06, t58, 71, 73, 85, 

101, 218-219, 238 
Transcendent judgments, 12- 

15, 19-21, 30-34, 42-44, 50-52, 

etc. 



Trial and error, 109, 139, 140, 
164, 166, 198, 213, 222, 234 

Truth, 4-6, 14, 23, 28, 37, 41, 
43, 81, 92, 100, 106 

Understanding, 93, 346 

Unity, 28, 39-54 passim, 65-68, 
75-80, 91, etc. 

Universals, 40-42 

Validity, chs. iii, ix, x, xvii, 

350-353 
Values, practical, 4, 38, 82, 88, 

188, 339 

—social, 65-66 

— theoretical, 23, 27, 339 
Verification, 27-28, 31, 34-35, 

93, 105, 176-177, 193, 203, 

266 

Words, 19, 20, 58, 187, 292 







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